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Lord Kelvin (1824-1907). 



ELEMENTARY PHYSICS 



A TEXT-BOOK FOR HIGH SCHOOLS 



BY 
LLOYD BALDERSTON, Ph.D. 

PROFESSOR OF PHYSICS AT THE WEST CHESTER STATE NORMAL SCHOOL 
WEST CHESTER, PENNSYLVANIA 



. PHILADELPHIA 
CHRISTOPHER SOWER COMPANY 



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LIBRARY of CONFESS* 
two GODies new***' 

SEP 8 i»ua 



Copyright, 1908 
Br Christopher Sower Company 



PREFACE. 



This book is intended for use in the last years of the high 
school. It supposes a knowledge of elementary algebra. 
In a few paragraphs geometrical theorems are referred to, 
but these may be omitted without breaking the continuity 
of the text The text is intended to accompany experi- 
ments by the instructor before the class, and to be supple- 
mented by laboratory work on the part of the students. 

Physics embraces a field so wide and so crowded with 
important facts and principles that it is hard to decide what 
to include and what to omit. The selection here offered is 
based upon fifteen years* experience in teaching physics to 
students of high-school grade. The writer has aimed to 
omit nothing of prime importance which can be brought 
within the range of students of the grade for whom the book 
is intended. In selecting among matters of less importance, 
and in illustrating laws and principles, an effort has been made 
to choose, as far as possible, things with which the average 
student is likely to be somewhat familiar, or with which he 
may easily acquaint himself. 

Many of the problems are based upon actual observation 
and measurement, and it is believed that none of them lead 
to impossible results. 

The tables are taken, with little exception, from the com- 
pilation of physical tables published by the Smithsonian 
Institution. 

(iii) 



ly PREFACE 

The writer is greatly indebted to Dr. Robert R. Tatnall, 
Assistant Professor of Physics at Northwestern University, 
who has critically examined the whole manuscript and 
made many valuable suggestions. A like acknowledgment 
is due to Dr. J. Franklin Meyer, Professor of Physics at State 
College, Pa., who has read a part of the manuscript. 

L. B. 

West Chester, 1908. 



CONTENTS. 



CHAPTER I. — Properties of Matter. 

PAGE 

Introductory. Measurement. General Properties of Matter. 

Law of Gravitation. Special Properties of Matter ... 9 



CHAPTER II. — Force and Motion: Work and Energy. 

Kinds of Motion. Vectors. Composition and Resolution of 
Velocities and Displacements. Acceleration. Measurement 
of Forces. Newton's Laws of Motion. Equilibrium of 
Forces. Work and Energy. Moment of Inertia. Falling 
Bodies. Friction. Resistance of the Air. Formulae for 
Energy. The Pendulum. Elementary Machines ... 19 



CHAPTER III.— Liquids. 

States of Matter. Free Surface of Liquid. Surface Tension. 
Pressure in Liquids. Floating Bodies. Density and Specific 
Gravity. Liquids in Motion. Water Machines .... 66 



CHAPTER IV.— Gases. 

Kinetic Theory. The Atmosphere. Balloons. Pressure of the 
Atmosphere. Barometer. Boyle's Law. Wind Power. 
Pneumatic Machines. Air-pump. Siphon. Pumps. Car- 
tesian D;' er 



(v) 



vi CONTENTS 

CHAPTER V.— Wave Motion. 

PAGE 

Periodic Motion. Simple Harmonic Motion. Phase, Composi- 
tion of Simple Harmonic Motions. Water Waves. Ripples. 
Air- waves. Speed of Longitudinal Waves. Waves in Strings. 
Interference. Stationary Waves 121 



CHAPTER VI.— Sound. 

Media. Sounding Bodies. Speed of Sound. Reflection of 
Sound. Musical Sounds. Siren. Pitch. Loudness. Quality. 
Manometric Flames. Forced and Sympathetic Vibrations. 
Resonance. Interference. Beats. Pipes. Strings. Chlad- 
ni's Figures. Voice. Hearing. Musical Scales. Harmony 
and Discord 137 



CHAPTER VII.— Light. 

Nature of Light. Media. Theories of Light. Shadows. Speed 
of Light. Photometry. Reflection. Visual Angle. Plane 
Mirrors. Concave Mirrors. Convex Mirrors. Caustic. Re- 
fraction. Index. Total Reflection. Lenses. Images by 
Convex Lens. Optical Instruments. The Eye. Color. 
Solar Spectrum. Bright Line Spectrum. Absorption Spec- 
trum. Spectroscope. Achromatic Lens. Rainbow. Com- 
plementary Colors. Colors of Opaque Objects. Inter- 
ference. Diffraction. Polarization 167 



CHAPTER VIII.— Heat. 

Heat a Form of Energy. Temperature. Thermometers. Ex- 
pansion by Heat. Law of Charles. Specific Heat. Mechan- 
ical Equivalent of "Heat. Change of State. Latent Heat. 
Clouds. Vapor Pressure. Critical Temperatures. Ice 
Machines. Distribution of Hea+ Conduction. Radiation. 
Heat Engines 218 



CONTENTS Vli 

CHAPTER IX.— Magnetism. 

PAGE 

Natural Magnets. Poles. Law of Magnetic Force. Unit Pole. 
Nature of Magnetism. Lines of Magnetic Force. The Earth 
a Magnet. The Compass. Declination. Dip .... 258 



CHAPTER X.— Static Electricity. 

Electrification. Attraction and Repulsion. Positive and Nega- 
tive. Conductors and Insulators. Charged Bodies. Gold- 
leaf Electroscope. Induction. Points. Unit Charge. Po- 
tential. Electrophorus. Influence Machines. Condensers. 
Lightning . 270 



CHAPTER XI.— Current Electricity. 

Simple Cell. Polarization. Electrolysis. Gravity Cell. Le- 
clanche Cell. Storage Cells. Resistance. Effect of Tem- 
perature on Resistance. Cell Arrangement. Ohm's Law. 
Heat Developed. Magnetic Effects of Currents. Galvan- 
ometers. Voltmeters and Amperemeters. Electro-magnets. 
Thermal Currents. Induced Currents. Lenz's Law. Induc- 
tion Coil. Self-induction. Magneto Machine. Commutator. 
Armatures. The Dynamo. Alternators. Applications of 
Electric Currents. Plating. The Arc. Incandescent 
Lamps. Transformer. The Telegraph. Motors. The 
Telephone. Electric Measurements „ 286 



CHAPTER XII. — Electro-magnetic Waves and Radio-activity. 

The Ether. Maxwell's Theory. Herz's Discoveries. The 
Coherer. Wireless Telegraphy. Kathode Rays. Rontgen 
Rays. Ionization of Gases. Electrons. Becquerel Rays. 
Radium 339 



TO THE STUDENT. 



An effort has been made in this book to frame such para- 
graph headings that in review work they will recall the sub- 
stance of the paragraph if it has been carefully read before. 
They may thus serve, in connection with the italicized parts, 
for a rapid topical review. 



(viii) 



ELEMENTAEY PHYSICS. 



CHAPTEE I. 

PROPERTIES OF MATTER. 

INTRODUCTORY. 

1. The word science comes from the Latin scio, "I know." 
It does not, however, have the same meaning as knowledge. 
The woodman who has spent his life among trees, and knows 
fifty species, their habits of growth, the character of their wood, 
and all the multitude of facts which intelligent observation 
reveals, may yet have less scientific knowledge of trees than 
a boy who. has had half a year of botany in a city school, 
and cannot call by name a single tree. The city boy will 
probably have learned that the tree derives much of its nour- 
ishment from the air through its leaves, a fact which would 
be likely to be unknown to the woodman. The scientific study 
of trees concerns itself with the relation of the parts of the 
tree to each other and the work which each does in contrib- 
uting to the life and growth of the whole, and with the relation 
of the tree to its surroundings and to the forces of Nature, 
Science is related, organized knowledge. 

2. There are many fields of scientific study. One great 
branch of science is mathematics. The truths with which 
pure mathematics deals are abstract, having no connection 
with any material things. Of all the sciences which concern 
themselves with the objects which surround us, physics is 
the most fundamental. It deals with the properties and con- 
duct of objects in general. Chemistry treats of the substances 
of which the things are made. It is impossible to distinguish 
sharply between physics and chemistry, and, on the other 
hand, astronomy is only a separate science because the objects 

(9) 



10 PROPERTIES OF MATTER 

with which it deals, the heavenly bodies, as we call them, are 
such a distinct class of things. The laws of physics apply to 
living things, while those phenomena which are related to life 
are the subject matter of biological science. Among the many 
problems of physics are such as these: Why smoke goes up 
the chimney, while a brick would fall down it; why oil rises in 
the wick of a lamp; why moisture collects on the outside of 
a glass of ice water in a warm room. 

3. Every department of science has its own technical terms, 
which must be accurately defined. These are often ordinary 
words, to which special meanings are applied. Thus, the 
words stem and fruit as used in botany include many things 
which we do not commonly regard as stems and fruits. 
Many of the terms of physics are thus familiar words whose 
scientific and non-scientific uses are nearly the same. Two 
of the most important of these terms are matter and force. 
Because the ideas which these words convey are so funda- 
mental, they are difficult to define. It is customary to 
say that matter is anything which occupies space, and this 
is perhaps as good a definition as can be given. Substance is 
used in speaking of matter of a definite kind. Wood, lead, 
and air are substances. A body is a definite portion of matter, 
as a pound weight, the water in a glass or the air in a room. 

4. A force is either a push or a pull. A force acting on 
matter tends to make it move or stop moving, or to change 
its motion in some way. It is clear that force can be exerted 
only by matter. The wind propels sailing vessels; falling 
water drives the mill; the horse pulls the carriage. In this 
discussion we are leaving the terms, space and motion, un- 
defined, and they are scarcely more fundamental than matter 
and force. 

5. When the Greeks observed that a stone falls more 
rapidly than a feather they inferred that this is because the 
stone is heavier, and so made the general statement that the 
speed of a falling body increases with its weight. This 
method of arriving at conclusions in regard to the behavior 
of things is no longer relied upon by scientists. It leads 



GENERAL PROPERTIES OF MATTER \\ 

too often, as in the case just cited, into serious error. If we 
think, from a train of reasoning, that a thing ought to behave 
in a certain way, we try it and see if it does. Nearly all 
the conclusions which have been reached by physicists are 
based upon experiment. It has been well said that an 
experiment is a question put to Nature. Our dependence 
on experiment is based on the belief that the same causes 
will always produce the same results. If an experiment is 
tried many times with exactly the same conditions, the result 
will always be the same. Apparent exceptions to this 
principle of the "constancy of Nature" are due sometimes 
to our inability to reproduce the conditions exactly, or to 
measure results accurately. Sometimes they are due to 
differences in the conditions of which we are not aware. 
Unexpected results, leading to minute examination of the 
conditions, have thus often led to important discoveries. 

6. A large part of the work done by physicists consists 
of measurement. In order to measure any quantity, it is 
necessary to select some other quantity of the same kind 
and of convenient size, called a unit of measure, and either 
by direct comparison or by some other means determine 
how many times it is contained in the quantity to be meas- 
ured. For instance, if we wish to measure the length of a 
table we may choose the foot as our unit, and, taking a 
rule one foot long, place it at one end of the table, mark the 
point to which it extends, move the rule along and mark 
again and so on. This is an example of the simplest mode 
of measurement. We may describe it briefly by saying 
that to measure a quantity is to find its ratio to the unit of 
measure. In stating the result of a measurement we use a 
pure number (the value of the ratio), and the name of the 
unit used. 

GENERAL PROPERTIES OF MATTER. 

7. Physical State. Matter exists in three physical states: 
solid, liquid, and gaseous. These words are in common 



12 PROPERTIES OF MATTER 

use with the same meaning which they have in physics. 
They will be discussed later. 

8. Extension. Matter occupies space. If we choose a 
point within a body, three lines can be drawn through the 
point, each at right angles to the other two, and some part 
of each line will be included in the body. The three dimen- 
sions of a body are thus at right angles to each other. If 
the body has a simple shape like a book, we specify its three 
dimensions as length, breadth, and thickness. These are 
measured in linear units, as inches or centimeters. In 
scientific measurements metric units are almost universally 
employed. The centimeter is one-hundredth of a meter. 
The meter was intended to be (and is very nearly) one ten- 
millionth of the distance from the equator to the pole. 
One meter is equal to 39.37 inches; 2.54 centimeters equal 
one inch. The units of area in the metric system are the 
squares whose sides are one centimeter, one meter, etc. 
They are called the square centimeter, square meter, etc. 
The units of volume are cubes, whose edges are the linear 
units and are called cubic centimeters, cubic meters, etc. 
Centimeter is abbreviated into cm.; square centimeter into 
sq. cm. or cm. 2 , and cubic centimeter into c.c. or cm. 3 
A length subdivided into equal parts to be used as a measure 
is called a scale. The ordinary meter-stick is a scale on which 
the centimeters are numbered, but the smallest division is 
a millimeter, or one-tenth of a centimeter. 

9. Mass. The whole quantity of matter in a body is its 
mass. The diminutive of mass (Latin moles) is molecule. 
In the case of a given substance, as for instance sugar, the 
molecule is the smallest particle of it, which retains its 
characteristic properties. If some sugar be dissolved in 
water, its molecules are separated from each other, but each, 
we believe, remains a molecule of sugar. All the molecules 
of the same substance are supposed to be of almost precisely 
the same size. In comparing two bodies of the same sub- 
stance, we may say that the one which has the greater 
number of molecules has the greater mass. We cannot, 



GRAVITY 13 

however, determine the actual number of molecules in any 
body. They are far too small to be seen by the highest 
power of the microscope. Their size has been estimated 
in various ways and the results agree fairly well. There are 
perhaps as many molecules in a drop of water as there are 
drops of water in the entire ocean. The unit of mass 
employed in scientific measurements was intended to be 
(and is very nearly) the quantity of matter in 1 c.c. of pure 
water at 4° C, the temperature at which its density is great- 
est. This unit is called the gram. 

10. Gravity. All matter attracts other matter. The force 
with which most small bodies attract each other is so slight 
as to be measured with difficulty. The attraction of the 
earth for bodies on its surface is one of the most familiar 
of facts. It is this attraction which causes things to have 
weight. It is called the attraction of gravitation, or, more 
briefly, gravity. Sir Isaac Newton 1 first investigated this 
force and formulated the law of universal gravitation: 

Every particle of matter in the universe attracts every other, 
the force between any two being proportional directly to the 
product of their masses and inversely to the square of the 
distance between them. The attraction of a homogeneous 2 
sphere for other bodies is exerted as if the mass of the 
sphere were all concentrated at its centre. Thus, the 
distance which we must use in discussing the attraction 

1 Sir Isaac Newton, Englishman, 1642-1717. Mathematician and 
philosopher of the first rank. His great book was written in Latin. 
Its title is commonly abbreviated into "The Principia." 

2 The earth is not homogeneous, but increases in density toward 
its centre. This must be true since the density of the earth as a whole 
is about twice as great as that of the surface rocks. For an object 
on or outside of its surface, the attraction of a sphere is the same as 
if its mass were all concentrated at its centre, provided only that the 
mass be symmetrically distributed about the centre. In the case of 
the earth, because of the increasing density as we descend, gravity 
at first increases. If we could go on toward the centre, it must after 
a time begin to decrease and become zero at the centre. 



14 PROPERTIES OF MATTER 

of the earth for bodies on its surface is the radius of 
the earth. 

11. It follows from this law that the weight of a body 
depends upon its place. If the same body were weighed 
with a sufficiently accurate spring balance at the North 
Pole and at the Equator, it would be found to be about 
2-g~o heavier at the pole than at the equator. This is chiefly 1 
because a body at the pole is nearer to the earth's centre 
by some 12^ miles, on account of the " flattening" at the 
poles. If the same object could be weighed on the moon's 
surface its weight would be about one-sixth of what it is 
on the earth. Its mass, however, would remain unchanged. 
The only convenient method of comparing masses is by 
weighing. We say that a body which weighs twice as 
much has twice as much mass. The law of gravitation 
as commonly stated assumes that weight is proportional 
to mass. 

12. The metric unit of weight is the gram weight, which 
is the attraction of the earth, that is the force exerted by tjie 
earth, on one gram mass at sea level in latitude 45°. This 
use of the same word to denote two units so different in kind 
sometimes leads to a confusion of ideas. Weight and mass 
are even more unlike than arcs and angles which are also 
measured by units having the same name, degree of arc and 
degree of angle. 

13. Density. Lead is said to be more dense than alumi- 
num. Density means quantity of matter in unit volume. 
If we use the gram as the unit of mass and the c.c. as the unit 
of volume, the number of grams in one c.c, found by dividing 
the number of grams in the mass of the body by the number 
of c.c. in its volume, is called the absolute density of the body. 
This has the same numerical value in the case of solids and 
liquids as their specific gravity, discussed in the chapter 
on Liquids. 

1 A part of the decrease in the weight of a body in passing toward the 
equator is due to the increasing centrifugal force (paragraph 68) which 
tends to make bodies fly off into space. 






POROSITY 15 

14. Inertia. It takes force to move anything and force 
to stop anything that is moving. This inability of a body 
to move or stop moving of itself is called inertia. A 
large body is harder to start and harder to stop than a 
small one of the same material. Inertia, like weight, is 
proportional to mass. If a stone weighing several pounds 
be held in the hand, it may be struck a violent blow with 
an ordinary hammer without hurting the hand. A piece 
of granite or other hard rock may be broken thus. If a 
small bit of stone be used in such a case, the hand would 
be severely bruised by a blow of the same force. The inertia 
of the heavy stone causes it to start slowly when struck, 
while the small one is made to start more rapidly and thus 
hurt the hand that holds it. If a rapidly moving wagon 
strikes a telegraph pole the driver may be hurled out, his 
inertia preventing him from stopping with the wagon. 

15. Indestructibility. Matter can neither be created nor 
destroyed. When wood is burned a small part remains 
solid, the ash, but nearly all passes off into the air in the form 
of gas, chiefly carbon dioxide and vapor of water. In 
every instance in which matter appears to have been de- 
stroyed it has only changed its form. This belief that 
matter is indestructible is often referred to in the phrase 
"conservation of matter." 

16. The properties thus far discussed may be called uni- 
versal properties of matter, since all matter possesses all of 
them. Beside these there are many others possessed by 
only some kinds of matter, or by some kinds to much greater 
extent than by others. 

17. Porosity. There are spaces between the molecules 
in the case of all kinds of matter. In the metals these 
spaces are too small to be observed in any way yet discovered. 
That they exist is proved by the fact that water may be 
forced through solid metals by sufficiently great pressure. 
In the case of air the molecules themselves occupy only a 
very minute part of the whole space which the air takes up. 
Sometimes the spaces which may be seen in wood, by the 



16 PROPERTIES OF MATTER 

unaided eye or with a magnifying glass, are called pores, 
and wood or unglazed porcelain is said to be porous while 
glass is not. In a broader sense, however, even the closest 
grained matter has pores. 

18. Elasticity. If a piece of glass tube be bent slightly 
and released, it returns to its original shape. The same is 
true of wood, steel, and most solids. They are said to be 
elastic. They have elasticity of form. If bent too far 
they may break or remain bent. The point beyond which 
they cannot be bent without breaking or permanent change 
of shape, marks their limit of elasticity. In the case of lead 
this point is reached so soon that unless we observe quite 
carefully we might say that lead has no elasticity of form. 
Liquids and gases have only elasticity of volume. If they 
are forced into a smaller space they expand again when the 
pressure is released. Elasticity of liquids and gases, so far 
as known, is without limit. Solids also have elasticity of 
volume, but for many of them it is limited. When a marble 
is dropped on a smooth stone it bounces, showing that the 
stone is elastic. A great enough pressure crushes stone. 

19. Elasticity is measured by the force with which the 
body tends to return to its original volume or shape when 
compressed or distorted. Because a piece of india-rubber 
may be easily stretched and returns to its original length, 
we sometimes say it is very elastic. In the strict sense it 
is far less elastic than a piece of steel wire of the same size, 
which may be stretched, but not so far as the rubber, and 
resists stretching with a far greater force. There should be 
another word to describe the property which is so highly 
developed in india-rubber. We might call it extensibility. 
Because air is so much more easily compressed than water, 
it is often thought of as being more elastic. In fact water 
is vastly more elastic than air, although far less compressible. 

20. Hooke's Law. The amount of bending or stretching 
of an elastic solid is proportional to the force applied, so 
long as its limit of elasticity is not reached. This fact is 
made use of in the ordinary " spring balance" or dynam- 



HARDNESS 17 

ometer (force measurer). The spaces on the scale are equal, 
showing that a force of 200 grams stretches the spring twice 
as much as 100; 300 three times as much, etc. Robert 
Hooke 1 was perhaps the first to call attention to this property. 
He stated it in Latin, "Ut tensio sic vis," which may be 
translated displacement is proportional to force. 

21. Tenacity. A body is tenacious which resists being 
pulled apart. Steel is perhaps the most tenacious known 
substance. Silk is more tenacious than cotton. In testing 
materials which are to be used for bridges or buildings, 
particularly steel, the measurement of tenacity is very 
important. A rod of a certain size, say 1 cm. square and 
10 cm. long, is clamped in the jaws of the testing machine 
and pulled with a gradually increasing measured force until 
it stretches and finally breaks. 

22. Ductility. A substance is said to be ductile when it 
can be drawn into wires, as iron, copper, and many other 
metals. It is possible to make platinum wires much too 
fine to be seen by the unaided eye. 

23. Malleability. Most metals are also malleable; that is, 
they may be beaten into thin sheets. Gold leaf may be 
made so thin that 300,000 sheets would be required to make 
a pile one inch thick. 

24. Hardness. Of two substances, that one is said to be 
harder which will scratch the other. Diamond is harder 
than glass; steel than slate. In the present state of our 
knowledge no satisfactory definition of hardness is possible, 
and no means of measuring it has been devised. 

25. We know so little about the molecular forces that 
many of the terms we use are difficult to define. Some 
substances, as molasses candy, may be bent if pressure is 
applied slowly, but will break if struck with a hard object. 
Things which break under sudden shocks are called brittle. 
Glass is made less brittle by being very slowly cooled. This 
process is called annealing. Some fibrous substances, as 
leather and green hickory wood are tough, as are many 

1 Robert Hooke, English Scientist, 1635-1703. 
2 



18 PROPERTIES OF MATTER 

metals. Some kinds of steel, when annealed, are tough; 
but if suddenly cooled from a high temperature they are 
brittle, and much harder than when annealed. Steel tools / 
springs, etc., are subjected to a process called tempering, 
by which they are brought to the degree of hardness required 
for the work they are to do. The floors of a building or the 
spans of a bridge need to be rigid; that is, not to bend under 
the loads imposed upon them. All solids have some rigidity, 
but none is absolutely rigid. The opposite of rigid is flexible. 
Threads are easily bent, but the finest thread requires some 
force to bend it. 

EXERCISES. 

1. Why does the wood-chopper lay small sticks on a 
" chopping block ?" 

2. Why is it possible to propel a boat with oars? 

3. Explain why a rifle-ball will make a clean hole in a pane 
of glass, while a bullet thrown by hand will shatter the glass. 

4. Compare the following substances in regard to hardness, 
toughness, tenacity and rigidity: glass, wrought iron, 
hardened steel, leather, hickory wood, copper, quartz, and 
celluloid. 

5. What property is of importance in the " straw-board" 
of a book-back? In the leather or cloth which covers it? 

6. Upon what property of matter does a clock-spring 
depend for its usefulness? A rope? 

7. What two properties of matter are important to the 
hammer? To a nail? To an anvil? 

8. How would you force a tight-fitting handle into a 
hammer ? Why ? 

9. A meteorite is found to weigh 1 kilogram. With what 
force was gravitation pulling it when it was 4000 miles 
above the earth's surface? 

10. The mass of the moon is about -fa of that of the earth, 
and its diameter is 3600 kilometers, while that of the earth 
is 13,187. If an object weighs 1 kilogram on the earth 
how much would it weigh on the surface of the moon ? 



CHAPTEE II. 

MOTION AND FORCE— WORK AND ENERGY. 

MOTION AND FORCE. 

26. Rest and Motion. The ideas conveyed by these two 
words are so simple and fundamental that satisfactory 
definition is impossible. We always use the terms relatively. 
A man sitting in a moving railroad train is in motion with 
respect to trees and fences along the line, while he is at rest 
in relation to the seats and other objects in the car. In 
general we say things are at rest when they do not move 
with reference to the earth. Of course the earth moves with 
reference to other members of the solar system, and such a 
thing as absolute rest is inconceivable. A point is in motion 
with respect to another when the line joining the two is 
changing in length or direction or both. 

27. Translation and Rotation. In general, our study of 
motion will involve solid bodies which have some appreciable 
size. A body has motion of translation only when a line 
joining any two points of the body preserves the same 
direction. This is the case with a railroad car (excepting 
its wheels) when moving smoothly over a straight track. 
A rod fastened to the car in such a manner as to point East 
and West, continues to point East and West as the car moves. 
If points on one straight line through the body remain at 
rest, and the direction of every other point of the body 
from this line continually changes, we have motion of pure 
rotation, or rotary motion. The fixed line is the axis, and 

(19) 



20 MOTION AND FORCE— WORK AND ENERGY 

each particle of the body not in this line describes a circle 
having its centre in the axis. The fly-wheel of a stationary 
engine, and the revolving parts of a sewing-machine or 
turning-lathe are examples of pure rotation. The wheel of 
a railroad car or other vehicle evidently has motion both of 
translation and rotation. 

28. Speed. We are accustomed to speak of the rate of 
motion of a railroad train in kilometers (or miles) per hour, 
of a glacier in meters (or feet) per day, etc. When we 
thus refer to the number of units of space traversed in unit 
time, without reference to the direction of motion, we are 
dealing with the speed of the body. In the case of a rotating 
body, the speed of different particles is different, being 
proportional to the distance from the axis. 

29. Velocity. If one train moves due East at the rate of 
40 miles per hour, and another due West at the same rate, 
their speeds are equal, but their velocities are opposite. 
Direction is a factor in velocity, and when two velocities as 
in the case mentioned are exactly opposite, we may express 
this difference by giving to one of them a positive sign, and 
to the other a negative sign. Thus, if a boat be rowed up 
stream at a rate which would carry it 6 kilometers per hour 
in still water, and the current of the river is 6 kilometers per 
hour, the sum of the velocities is + 6 — 6 = 0. When a 
body moves in a straight line with uniform speed, it has 
also uniform velocity, but if it describe a curved path 
with uniform speed, its velocity is not uniform since its 
direction is continually changing. Velocity in the case of 
a rotating body may be stated by giving the number of revo- 
lutions per unit of time, or the length of time required to 
make one revolution, or the fraction of a revolution which 
takes place in unit time. In any case, the thing measured is 
an angular velocity. Thus the earth rotates through 15° in 
an hour; the fly-wheel of an engine makes so many revolu- 
tions per minute ; the moon revolves on its axis in 27 J days. 

30. Vectors. Velocities in common with other quantities 
which have both magnitude and direction, are called vector 



THE COMPOSITION OF VELOCITIES 21 

quantities. Such a quantity may be conveniently repre- 
sented by a terminated straight line, showing by its length 
the magnitude of the vector, and by an arrow-point the 
direction in which it is to be measured. Much of the mathe- 
matics of vectors is very difficult, but some important facts 
about them are easily understood. 

31. Addition of Vectors. The addition of two vectors 
whose directions are the same or opposite is effected simply 
by finding their algebraic sum, as has just been shown. If 
the directions are neither the same nor opposite, the signs 

f and — will not suffice to indicate their difference in direc- 
tion, but we may still add them graphically. If a boat be 
urged directly across a stream with a velocity of 100 meters 
per minute, and the stream flows at the rate of 100 meters 
per minute, we may determine the sum of these two vectors 
or the resultant velocity, by a simple construction. Let 
be the starting point of the boat. Suppose 
OE to represent the distance it would travel 
in one minute across the stream if there were 
no current, and OA the equal distance it 
would travel down stream in one minute 
if not urged across. The boat will actually FlG j 

do both of these things. It will in one min- 
ute travel across the stream the distance OE and down it 
the distance OA. The actual path described will be OR, 
the diagonal of the square. OR is the resultant velocity, 
and is the sum of the vectors OE and OA. Imagine 
the boat to be rowed the distance OE in still water, 
and then the rower to stop and the water to flow for 
one minute at the same rate at which the boat was rowed. 
The paths described would be OE and ER, and the net 
result would be the same as if the boat had traversed the 
path OR. 

32. The Composition of Velocities by the method just 
described is equally convenient in cases where the angle 
is not a right angle, and for velocities which are not equal. 
Suppose a boat rowed Northeast with a velocity of 6 kilo- 




22 



MOTION AND FORCE— WORK AND ENERGY 




Fig. 2 



meters per hour, and carried South by the current with a 

velocity of 4 kilometers per hour. Draw OA and OB, 

making an angle of 135°, OA being 6 units long, and OB 

4 units. Complete the parallelogram and 

draw OR, which is the vector sum. If, 

as before, we suppose the boat to move 

first over OA, and then over AR, the 

net result is the same as when it moves 

over OR. The vector sum of two sides 

of a triangle taken in order is the third 

side. The triangle construction applies 

to all cases to which the parallelogram 

method is applicable, and involves less 

drawing. 

If three or more velocities in the same plane are involved, 
their sum is equally easy to find. Suppose a boat rowed 
Northeast with a velocity of 6 kilometers 
per hour to be at the same time carried by 
the wind Southeast at the rate of 2 kilo- 
meters per hour and South by the current 
at the rate of 4 kilometers per hour. A 
construction as shown gives OR as the 
resultant velocity. Any side of a polygon 
is the vector sum of all the others. By 
this method of the polygon of velocities, 
velocities may be compounded. 

33. Composition of Displacements. The 
same method may be applied to find the 
sum of several displacements, without ref- 
erence to when or at what rate (constant 
or variable) they take place. Thus, if a 
body is moved North 10 feet, then West 
6 feet, then South 15 feet, the vector sum 
may be found by means of a polygon, as 
shown. AD is the vector sum of AB, 
BC, and CD, whenever and however those displacements took 
place. 



•4 

Fig. 3 
any number of 
B 



m 



A 



Fig. 4 



ACCELERATION 



23 




Fig. 5 



34. Resolution of Velocities. If a vessel sails Northeast, 
it is changing both its latitude and its longitude, and if we 
know the rate of sailing we can compute both how rapidly 
it is receding from the equator and 
how rapidly it is travelling eastward. 
Let OA represent the path of the ship 
for an hour. Draw OB due North and 
OC due East, and complete the square. 
(The portion of the earth's surface 
involved being so small we may regard 
the figure as a square without serious 
error.) Now OB represents the velocity toward the North and 
OC or BA toward the East. Let OA = 14.14 kilometers. 
Now because OB A is a right-angled triangle, OB 2 + BA 2 
= OA 2 , or since OB = BA,2 OB 2 = 
OA 2 = nearly 200. Then OB 2 is nearly 
100 and OB is nearly 10. Therefore 
the ship is moving North with a veloc- 
ity of 10 kilometers per hour and East 
at the same rate. If the angles of our 
figure are not right angles, the calcu- 
lation involves trigonometry, but by 
construction and measurement any 
velocity may be resolved into com- 
ponents in given directions. To re- 
solve the velocity OA into two components, parallel to DB 
and DC, draw OF and OE parallel to DB and DC. Through 
A draw AG and AH parallel to OF and OE, respectively. 
Now H and OG are the required components. 




Fig. 6. — Resolution of 
velocities. 



FORCE. 



35. Acceleration. Thus far we have considered motion 
without reference to the causes which produce it. Motion 
is produced by force. If a force, having set a body in motion, 
continue to act upon it, the body will move more and more 



24 MOTION AND FORCE— WORK AND ENERGY 

rapidly. The increase of velocity per unit time is called 
the acceleration due to the force, and if the force is constant 
the acceleration will be uniform. 

36. Newton's First Law of Motion. If the force after a 
time ceases to act, the body tends to move on with uniform 
velocity, because the same inertia by virtue of which it is 
unable to start itself, makes it unable to stop when it is 
started. Newton expressed these facts in his first law of 
motion, which may be stated thus: A body at rest remains 
at rest, and a body in motion continues to move with uniform 
speed in a straight line unless acted on by a force. Of course 
no body moves with uniform speed in a straight line in con- 
sequence of its inertia, except in the special case where the 
forces acting on it balance, because no body is free from 
the influence of forces. The second part of the law may be 
said to express the universal tendency of moving bodies to 
move with uniform speed in a straight path. If a stone is 
whirled by a string and the string breaks, the stone "flies 
off at a tangent;" that is, its path is for a short section 
nearly straight, compared with its previous course. 

37. Measurement of Forces. It has been stated that the 
gram is the unit of weight. Since weight is simply the force 
with which the earth pulls matter, the gram and other units of 
weight are also units of force. They are called gravitational 
units because they depend upon gravity and vary with it. 
Although not quite invariable, these are much the most 
convenient units, and they are universally employed for 
practical purposes. The horse pulls the carriage with a force 
of so many pounds or kilograms. 

38. Absolute Units of Force. In practice no force acts 
alone upon a body, but we may in many cases determine 
separately the effects produced by the different forces. 
These effects may sometimes be measured by the mass of 
the body acted upon, and by the amount of motion pro- 
duced. Such a force as can give to unit mass in unit time 
unit quantity of motion would then be called unit force. 
Such a unit would be invariable, since it depends for its 



GRAPHIC REPRESENTATION OF FORCES 25 

value on mass, distance, and time, which are measured in 
invariable units. Using the gram, centimeter, and second as 
units of mass, length, and time, we have the unit of force 
called the dyne (from the Greek dynamis, force), which is 
used in accurate scientific work, and is an absolute unit. 
A dyne is that force which, acting for one second upon one 
gram ?nass, will give to it a velocity of one centimeter per 
second. To give to two grams in one second a velocity of 
one centimeter per second would require a force of two 
dynes, and in general the product of the number of units in 
the mass by the number of units of acceleration (i. e., velocity 
gained per second) gives the number of dynes in the force. 
This is expressed in the formula f = m a. If a mass of 100 
grams be suspended by a very long thread, it may move 
a short distance horizontally without rising much. A force 
acting horizontally on it would be almost entirely concerned 
in overcoming its inertia, at first. Suppose the suspending 
string 10 meters long, and that a horizontal force acts on 
the 100 gram mass for one second and then ceases. If the 
body moves 1 cm. in the next second, the force acting would 
be almost exactly 100 dynes. 

39. Momentum is generally defined as quantity of motion. 
It is found by multiplying the numerical values 1 of mass 
and velocity. Thus a body weighing 1 kilogram and having 
a velocity of 10 meters per second has 10 units of momentum, 
as much as if the mass were 5 kilograms and the velocity 
2 meters per second. 

40. Graphic Representation of Forces. Forces, like veloci- 
ties, are vector quantities, since they have both direction 
and magnitude. In order to define the effect produced by a 
force completely, its point of application must also be known. 
Forces may be represented by straight lines, and they 
may be compounded and resolved in much the same manner 
as velocities. 

1 When two things are multiplied together one of them must be a 
pure number. For the sake of brevity, however, we often use such 
expressions as "mass times velocity." 



26 



MOTION AND FORCE— WORK AND ENERGY 




Fig. 



B TR 

7. — Parallelogram of 
forces. 



41. Composition of Concurrent Forces. If several forces 
whose directions differ are applied at the same point, they 
are said to be concurrent. Forces applied at various points 
of a body are also concurrent if th^ir lines of direction inter- 
sect at a common point. We shall 
consider only those cases where the 
forces lie in one plane, although 
the method may be applied to all 
cases. Let the concurrent forces 1 A 
and B act on the point 0. Their 
resultant R is found in the same 
manner as the resultant of two velocities. Imagine a foot- 
ball kicked toward B and at the same time toward A with 
a force twice as great. The resultant force, equal to about 
2| times B, would impel the foot-ball toward R. This con- 
struction is often called the paral- 
lelogram of forces. As in the case 
of displacements and velocities the 
triangle construction may be used. 
If more than two forces are acting, 
the same method may be applied. 
In the figure R f is the resultant of 
A and B, and R is the resultant 
of R' and C. Thus R is the result- 
ant of A, B, and C. OR is the 
vector sum of OA, AR ; , and R'R, in which AR' = B and 
R'R = C, in magnitude and direction. The polygon method 
gives the same result more simply. Draw AR' parallel and 
equal to B, and then R'R parallel and equal to C. Com- 
pleting the polygon by joining OR gives the resultant. 

42. Resolution of Concurrent Forces may be effected in the 
same manner as resolution of velocities. When a body rests 
on a sloping surface the force exerted on it by gravita- 
tion may be resolved into two components, one parallel 
to the surface tending to make it slide, and the other per- 

1 Forces are conveniently named by a single letter, placed at the 
arrow-head. 



^i? 




Fig. 8 



IMPULSIVE FORCES 



27 




pendicular to the surface. Let be a body weighing 
2 kilograms, resting upon the inclined plane AB. Then 
OG, a vertical line 2 units 
long, may represent the force 
exerted on the body by 
gravity. Draw OC parallel 
and OD perpendicular to the 
plane. Through D draw GE A ( - r 

parallel to OD and GF paral- 
lel to OC. Now the number FlG - 9 
of units in OE shows the force in kilograms which urges 
down the plane, and in like manner OF represents the 
force against the plane. 

43. Newton's Second Law of Motion. Experience shows 
it to be true, as we have assumed in discussing composition 
of forces, that when several forces act simultaneously each 
produces its full effect as if the others were not acting. 
This fact is embodied in Newton's Second Law of Motion. 
A literal translation of the Latin of Newton's Principia is 
about as follows: Change of motion is proportional to the 
moving force impressed, and takes place in the direction in 
which this force acts. It is clear that motion here means 
momentum, and not merely velocity. A body which is 
projected horizontally from the top of a tower will move 
with uniform speed in a horizontal direction because of 
its inertia, but at the same time it will fall with increasing 
speed because of the attraction of gravitation. If the 
tower stand on level ground, the body will reach the earth 
in the same time that it would take to fall vertically. The 
horizontal speed depends upon the intensity of the projecting 
force and the mass of the body. The product of mass by veloc- 
ity gives us the measure, so to speak, of the projecting force. 

44. Impulsive Forces. In the instance just cited, the body 
having been at rest, the projecting force produced its whole 
effect in a time too brief to be examined in detail, and so 
the change of horizontal momentum is simply the whole 
horizontal momentum which the body possesses while in 



28 MOTION AND FORCE— WORK AND ENERGY 

flight. The force of gravity, acting continuously, causes a 
continuous increase in the vertical momentum. 

45. Newton's Third Law of Motion. When a horse is pulling 
a carriage, the traces are pulled back by the carriage just as 
hard as they are pulled forward by the horse. This axio- 
matic statement for continuous forces is expressed in the 
third of Newton's laws of motion : "To an action there is always 
a contrary and equal reaction; or the actions of two bodies 
upon each other are always equal and oppositely directed." 
In the case of impulsive forces we can only measure the 
action and reaction by momentum. If a moving marble 
strike " fairly" a stationary one of equal size, the one which 
was moving will stop, having given all its momentum to 
the other. When a bat strikes a ball the ball receives as much 
momentum as the bat loses, but the bat does not in general stop. 

46. Equilibrium of Forces. If two forces are equal and 
opposite, their resultant is zero, and the forces are said to 
balance each other, or to be in equilibrium. A pail weighing 
10 kilograms is carried by a man. Gravity exerts a down- 
ward force of 10 kilograms, and t 

the man exerts an equal upward -^N. 
force. The pail neither falls ^^ 

nor rises. The two forces are 
in equilibrium. A single force 
may hold two or more in equi- 
librium. Let R be the result- 
ant of A and B. If a force R', 
equal and opposite to R be ap- 
plied at it will hold A and B in equilibrium. In order, 
therefore, to find a force which shall hold any concurrent 
forces in equilibrium, determine their resultant. A force 
equal and opposite to this will be the required force. 

47. A book lying on a table is in equilibrium. The force 
of gravity pulling it down is opposed by an equal and opposite 
resistance on the part of the table. Resistances are measured 
in the same way as forces arid may be called forces. If one 
hold a weight on the palm of his hand, he is quite conscious 



MOMENT OF A FORCE 



29 



of exerting a force in supporting the weight against the action 
of gravity. Some modern writers describe the relations of 
the book and table by saying that there is a state of stress 
between the bodies, using the term stress to express in a 
general way the interactions of bodies in contact. 

48. Parallel Forces. If two or more forces act at the same 
point and in the same direction, their resultant is simply 
their sum. Several boys pull a sled up hill by a rope. The 
whole pull on the sled is the sum of the pulls exerted on the 



A 



B 



£—£--* 



Fig. 11. — Composition of parallel forces. 

rope by the several boys. If, however, some of the forces 
are in the opposite direction, we must take the algebraic 
sum, calling the forces in one direction positive and the others 
negative. In the figure let A = — 2, B = — 1, C = 1, D = 3, 
and E — 4. Then the resultant R = 5. 

49. Moment of a. Force. If several non-concurrent forces 
are applied at different points, they will in general tend to 
produce rotation. In Fig. 12 the forces A, B, and C in the 





Fig. 13 

same plane 1 applied to the body M will tend to cause it to 
rotate into such a position that the lines of direction pass 
through a common point. In Fig. 13 the forces are repre- 

1 If the forces are not in the same plane, the problem becomes very 
complex, and such forces have, in general, no single resultant. 



30 



MOTION AND FORCE— WORK AND ENERGY 



sented as acting in the same direction as before, and the 
body rotated so as to bring the forces into concurrence. 
The forces now act as if all were applied at and the body 
tends to move (with motion of translation only) in the 
direction of the resultant of the forces. The ability of a 
force to produce rotation is called its moment, which must 
not be confused with momentum. 

Moment pertains to a force, and momentum to a mass. 

50. In order to measure the moment of a force, we must 
first determine its lever arm, which is the perpendicular 
distance from the axis of rotation to the line of direction 
of the force. This supposes an axis of rotation at right angles 
to the plane or planes of the forces. We shall consider only 
the case in which the forces are in one plane and shall call 
the point in which the axis of rotation intersects this plane 
the centre of rotation. The figures represent a disk pivoted 





Fig. 14. — Moment of a force. 



at C and acted upon by a force A whose direction is constant, 
applied at 0. 

In 1, Fig. 14, CO A is a right angle, and CO is the lever 
arm of the force. The product of the force by its lever arm 
is the moment of the force. In 2 the moment is less than 
in 1, because the lever arm CB is less. In 3 the moment 
is 0, because there is no lever arm. These diagrams illus- 
trate the action of the piston and connecting rod of an engine 
upon the fly-wheel. At two points of the revolution the 
moment of the force of the piston is zero and at two points 
reaches a maximum. The inertia of the fly-wheel carries 
it past the "dead points." 



COMPOSITION OF PARALLEL FORCES 



31 





4 



Fig. 15 



aJR' 



51. Composition of Parallel Forces. Parallel forces acting 
on a body tend in general to produce rotation and transla- 
tion. In both these instances (Fig. 15) the forces tend to 
produce clockwise rotation, and 
translation in the direction of 
their resultant. In finding the 
effect of two or more parallel 
forces, we have to determine not 
only the intensity and direction 

of the resultant, but also its point of application. The direc- 
tion of the resultant is that of the preponderating forces, and 
its intensity is the algebraic sum of all the forces. 

52. The point of application is best determined by means 
of moments. Let the parallel forces A = 2, B = 3, C = 5, 
and D = 4 units, be applied as shown to a rigid body. Then 
the resultant R will be in the 

direction of A, C, and D, and will 
equal 8 units. Let the points of 
application of A and B be 15 cm. 
apart, of B and C 10 cm., and of 
C and D 40 cm. To find the point 
of application of R. Let it be x 
cm. from 0, the point of applica- 
tion of D. Assume acting at this 
point a force R', equal and oppo- 
site to R. It will hold the system 
in equilibrium, and therefore the 
sum of the moments of A, B y C, 
and D and R' with respect to any 
centre must be zero. If it were 
not so the body would revolve 
about some point as a centre. 
Take as a centre of moments. 
The moment of D is zero because its lever arm is zero. 
That of C is 40 X 5 = 200; that of A, 65 X 2 - 130, and that 
of B, — 3 X 50 = — 150. That of R' is — 8x. The sum 
of these is equal to zero; 180 — Sx = 0;x = 22 J. There- 



+B 



\A 



>o 



3E 



W 



i* 



Fig. 16 



32 MOTION AND FORCE— WORK AND ENERGY 

fore the point of application of the resultant is 22 \ cm. 
from 0. 

53. Couple. If two forces equal and opposite are applied 
at two points of a body, their resultant is zero. They can 
therefore cause no motion of translation, but can only cause 
rotation. Such a pair of forces is called a couple. The 
forces acting on a compass needle are a couple. One pole 
is pulled toward the South, and the other toward the North 
with forces exactly equal. 

54. Centre of Gravity. All the parallel forces exerted by 
gravity upon the particles of a body may be replaced by a 
single force equal to their sum, applied at a point which 
may be determined for bodies of geometrical shapes by an 
extension of the method above described. This point of 
application of the resultant of all the forces exerted by gravity 
upon the particles of a body is called the centre of gravity 
of the body. It is clear that if a force equal and opposite 
to the resultant be applied at the same point, the two will 
be in equilibrium. The centre of gravity of a uniform 
homogeneous rod is at its middle point. The blacksmith 
finds the middle of a rod of iron by balancing it on the edge 
of a tool. If geometrical figures be cut from flat, thin card- 
board, their centres of gravity may be easily determined. 
The centre of gravity of a circle or regular polygon is at its 
centre, of a parallelogram at the intersection of its diagonals, 
of. a triangle on a line joining a vertex with the middle point 
of the opposite side, at a point twice as far from the vertex 
as from the opposite side. If a pin be stuck through at the 
centre of gravity, the figure will balance upon the pin in any 
position. 

55. Equilibrium of Bodies; One Point of Support. A body 
supported at its centre of gravity is in neutral equilibrium. 
The supporting force and the force of gravity being applied 
at the same point there is no tendency to rotation, and if 
the body be disturbed it will not return to its previous 
position. If the point of support be elsewhere than at the 
centre of gravity, the force of gravity has a moment with 



mm 



EQUILIBRIUM OF BODIES; ONE POINT OF SUPPORT 33 

respect to the point of support as a centre of rotation for 
every position of the body except two, 1 and 3 in Fig. 17. 
When the body is in position 1, it is in stable equilibrium. 
If displaced slightly, as in 2, the force of gravity has a 
moment, G X PK, with respect to the point of support 
P, which tends to cause rotation and bring the body back 




Fig. 17. — Equilibrium of a suspended body. 

to position 1. If the centre of gravity is directly above 
the point of support, a slight displacement gives G a moment 
which tends to increase the displacement and bring the body 
to position 1. Position 3 represents unstable equilibrium. 
The vertical line through the centre of gravity is called the 
line of direction. 

56. The centre of gravity of an irregular flat body may 
be readily found. Make a small hole near one edge of an 
irregular piece of card- 
board. Let it hang from 
a pin stuck through the 
hole. Hang a bit of stone 
or metal to the pin by a 
string. Trace across the 
card with a pencil the 
direction of the " plumb- 
line. " The centre of grav- 
ity must lie in this line; 
otherwise the card would 
revolve about the pin. Choose a second point of support, as 
P' in the figure, and repeat. Now the centre of gravity is 
C, since a point which lies in each of two lines must be 
3 




Fig. 18. — Centre of gravity of a 
flat body. 



34 



MOTION AND FORCE— WORK AND ENERGY 




their intersection. Test the result by thrusting a pin through 
C. If the work has been carefully done, the card will hang 
in any position. 

57. Equilibrium; Several Points of Support. If a body rest 
on a plane it must in general have several points of sup- 
port. If these points be not in a straight line, the polygon 
made by joining the outer ones is called the base. Thus 
the base of an ordinary chair is a 

quadrilateral. If the line of direction ,''~""^X 

fall within the base, the body is in 
stable equilibrium, and it is more 
stable as the base is made larger. Sup- 
pose the figure to represent a cross- 
section of a body through its centre of 
gravity, C, A and B being two points 
of contact with the plane. If the body 
be displaced as represented by the 
dotted lines, the centre of gravity 

will have risen to C ', and the force of gravity will have a 
moment, G X AK, tending to bring the body back to its 
former position. If, however, the body be tilted so far that 
the line of direction falls beyond A and released, it will fall 
over instead of returning to its original position. 

58. The Measure of Stability for a body of given weight 
is the distance through which the centre of gravity must 
be raised in overturning 
the body. Thus a brick 
is most stable when lying 
on its broadest face. 

The dotted lines show 
how far it may be tilted 
in each case without 
overturning, and C'K is 
the distance the centre 
of gravity must be raised 
to overturn it. The stability of a body is also increased by 
placing the centre of gravity low. Compare the brick 



7 

i / 
/ 


I 

$ 
f 

i 








cL 

i 
i 
i 


til 

/ 


A 


i 
f 


< 


eA- 

< -S 1 






Fig 20.— Stability of a brick. 



NEUTRAL EQUILIBRIUM OX A PLAXE 



35 



with an object of the same size, shape, and weight made 
partly of wood and partly of lead, placed as shown. It may 
be tilted much farther without overturning. Tumbling dolls 







Fig. 21 

are sometimes made on this 
principle. A wagon loaded 
with stones is much more 
stable than the same wagon 
loaded with the same weight 
of hay. C is the centre of 
gravity of the wagon when loaded with hay, and C when 
loaded with stones. The load of stones may be driven safely 
along a hill-side on which the load of hay would overturn. 
59. Neutral Equilibrium on a Plane. A pencil may be 
balanced on its point for an instant, but as soon as it begins 
to move, the centre of gravity is lowered, and it falls. The 
position is an unstable one, and such a condition is sometimes 
called unstable equilibrium. The forces are 
balanced, but the slightest displacement per- 
manently destroys the balance. If, however, 
the pencil be laid on its side on a table, its 
centre of gravity neither rises nor falls with 
a slight displacement. The equilibrium of 
a homogeneous round body resting on a 
horizontal plane is neutral. The base is a straight line in the 
case of the cylinder and cone, and a point in the case of the 
sphere. In either case the line of direction passes through the 
base and the conditions are not changed by moving the body. 




Fig. 23. — Neutral 
equilibrium. 



36 MOTION AND FORCE— WORK AND ENERGY 

60. A small displacement raises the centre of gravity of 
a body in stable equilibrium, and lowers that of a body in 
unstable equilibrium; but if the equilibrium of the body be 
neutral, the centre of gravity neither rises nor falls when the 
body is moved. 

WORK AND ENERGY. 

61. Work is a familiar term, and its use in physics is 
entirely consistent with its customary meaning. When a 
hod-carrier takes bricks up a ladder he does work. The 
amount of work depends upon the number of bricks and the 
height to which they are carried. The work done in raising 
a kilogram 1 meter is sometimes called a kilogram-meter. 
The corresponding unit for the pound and foot is the foot- 
pound. In any case, work done is measured by the product of 
force acting and distance through which it acts, as expressed 
in the formula, W = FS. Corresponding to the gravitational 
units of force we have the various practical units of work, 
including kilogram-meter, foot-pound, and foot-ton. An 
absolute unit is the erg (from the Greek ergon, work), the 
amount of work done by 1 dyne acting through 1 cm. This 
is a very small unit. About 98,000,000 ergs make a kilo- 
gram-meter. 

62. Energy is usually defined as the ability to do work. 
Here, again, the common use of the word is consistent with 
its scientific use. The most energetic man is the one who 
can do the most work in a given time. The water in a mill- 
pond possesses energy; it can do work in turning the wheels 
of the mill. The wind possesses energy because of its motion ; 
it can turn the wind-mill and do work. Energy is measured 
in terms of the same units as work; the erg, foot-pound, etc. 
Since energy is the ability to do work, the measure of the 
energy possessed by a body is the amount of work which 
it can do. If we could frame a satisfactory independent 
definition of energy, we might define work as transfer of 
energy. In lifting a weight of 10 kilograms 1 meter, we 






POT EXT I AL AND KINETIC ENERGY 



37 



do 10 kilogram-meters of work upon it by expending our own 
energy, and give 10 kilogram-meters of energy to the weight. 

63. Force and Energy are often confused. Forces do work, 
but there is no necessary relation between the force acting 
and the quantity of work done. A small boy can carry a 
ton of coal up out of the cellar, a little at a time. A man, 
exerting twice as much force, could bring twice as much 
coal each time and make half as many trips. The smaller 
force must move over a greater space than the greater one 
in doing a given amount of work. A rock lying on the ground 
is acted on by the force of gravity, but it has no energy 
which can be used, because it cannot fall any farther. On 
the other hand, bodies may possess energy and not be exert- 
ing force. A bullet flying through the air possesses energy 
due to its motion, but is exerting no force (if we except 
the pushing aside of the air), and its energy is not due to 
force now being exerted upon it. Coal, as it lies in the bin 
or in the earth, possesses a great store of energy which seems 
to have no present relation to any kind of force. Energy 
is a more complex thing than force, sometimes including 
force and distance as two equally important factors. 

64. Potential and Kinetic Energy. A body in motion 
possesses energy, since it will take work to stop it. The 
inertia of the moving body tends to keep it moving, and a 
force must be applied to do work upon it to cause it to stop. 
It takes a large amount of work to stop a rapidly moving 
railroad train. The energy which a body possesses in con- 
sequence of its motion is called kinetic energy. The wind 
has kinetic energy; so have a cannon-ball in flight, and a 
hammer in motion. Kinetic energy is often called energy 
of motion. All other kinds are called potential energy. 
A clock weight wound up and the water in a mill-pond have 
potential energy. They can do work in falling. Energy 
of position describes such instances as these. In many 
cases, however, that term does not apply to potential energy. 
In some sense it describes the condition of a wound-up 
clock spring, but in no literal sense does it apply to the 



38 MOTION AND FORCE— WORK AND ENERGY 

potential energy contained in coal. Coal when burned 
gives out heat, which may be made to produce steam to 
drive an engine and so do work. The word potential usually 
implies stored, to be used in the future, or undeveloped and 
likely to be realized in the future. 

65. Potential is from the Latin potens, which often means 
being able. We may say of a thoughtful child that he is a 
potential philosopher, or that arid lands have great potential- 
ities. We are apt to think of kinetic energy as something 
which cannot be stored, but must be used at once or it will 
go to waste. The wind and the current of a stream are 
examples. But the earth as it moves through space has a 
vast amount of kinetic energy, which is likely to remain 
stored there for untold ages. So potential energy does not 
always remain stored. The projectile at the top of its flight 
has potential energy, but does not retain it. 

66. Transformation of Energy. As it leaves the hand, a 
ball thrown into the air has kinetic energy. As it rises, the 
force of gravity works upon it, causing it to move more and 
more slowly. When it reaches the top of its flight it has 
potential energy equal in amount to the work done upon it 
by gravity during its rise. The kinetic energy has been 
transformed into potential. As it falls, this potential energy 
is gradually transformed back into kinetic, and when it 
strikes the ground its energy is wholly kinetic. If it strikes 
in soft earth so as not to rebound, the kinetic energy is all 
converted into heat, which raises the temperature of the sur- 
rounding earth slightly. Heat is molecular kinetic energy, 
and is capable of being changed into other forms and doing 
mechanical work, oftenest through the medium of steam. 

67. Moment of Inertia. The kinetic energy of a rotating 
body depends not only upon its angular velocity and upon 
its mass, but upon the distribution of the mass with reference 
to the axis of rotation. The long cylinder A (Fig. 24) has less 
kinetic energy in rotating about its axis than the disc B, 
having the same mass and making the same number of 
turns per minute. The parts of the rotating body which 



IS 



CENTRIFUGAL FORCE 39 

are farther from the axis have greater speed and so more 
energy than those nearer the axis. The product of the mass 
of a particle by the square of its distance from the axis 
is called the moment of inertia of the particle, and the sum 
of these products for all the particles of the body is the 
moment of inertia of the body. It may be shown that the 
kinetic energy of a rotating body is equal 
to one-half the product of its moment of 
inertia by the square of the angular veloc- 
ity. This is precisely analogous to the 
kinetic energy of motion of translation, 
which is equal to one-half the product of 
mass by the square of velocity, as proved *^ 
in paragraph 100. Fly-wheels are attached, Fig. 24 

to many kinds of machines because by stor- 
ing energy when for any reason the machine tends to go 
faster than usual, and giving it out again when it tends to 
go slower, the speed is kept nearly constant. The fly-wheel 
should be as large as is convenient, and should have a large 
part of its mass in the rim, since the moment of inertia is 
made greater by increasing the average distance of the mass 
from the axis. 

68. Centrifugal Force. Fly-wheels sometimes burst, be- 
cause the tendency of the material in the rim to move, in 
consequence of its inertia, in a straight line instead of a 
curve is so strong as to overcome the cohesion of the wheel. 
This force, directed away from the centre of rotation, is called 
centrifugal force. It increases as the angular velocity in- 
creases, and also with increased radius of the circular path. 
For a given linear speed, however, centrifugal force increases 
with decreasing radius; that is, increasing curvature. A 
train running at 45 miles an hour is more likely to be over- 
turned in going around a sharp curve than in running 
over a nearly straight track. These points may all be 
illustrated by whirling a stone tied to a string and varying 
the length of the string and the speed of rotation. The 
sling, used by the ancients to throw missiles, is illustrated 



40 MOTION AND FORCE— WORK AND ENERGY 

by letting go the string when the stone is whirling rapidly. 
The stone flies off in a path which would be straight but for 
the attraction of gravitation, and is tangent to the circle 
in which it moved before. A figurative use is often made 
of this fact. One " flies off at a tangent" when anger cuts 
the cords of self-control. As has already been noted, cen- 
trifugal force helps in making bodies lighter at the equator 
than at the poles. 

69. Rate of Doing Work. An engine capable of doing 
33,000 foot-pounds of work per minute is called a one horse- 
power engine. This rate of working is called one horse-power, 
and is a unit of power. The corresponding unit in the 
C. G. S. absolute system is the kilowatt, equivalent to about 
lj horse-power. One thousandth of a kilowatt is a watt, 
equal to 10,000,000 ergs per second; 746 watts are equivalent 
to one horse-power. 

70. Conservation of Energy. While energy may undergo 
numberless transformations, we believe that it is as incapa- 
ble as matter of being created or destroyed. This belief grew 
into general acceptance during the middle third of the nine- 
teenth century, and has now for a generation been an undis- 
puted article of our scientific creed. We cannot always trace 
with certainty all of the changes which energy undergoes, but 
countless observations and measurements support the propo- 
sition that energy cannot be created and is indestructible. 

The water-power and wind-power which drive our mills 
are directly traceable to the energy of the sun, as are most 
of the activities of the earth. There is a general tendency on 
the part of other forms of energy to degenerate into heat, 
which is not easily available for doing work. If, instead of 
passing over a wheel and doing work, the water of a stream 
simply falls over the dam, its temperature is slightly raised, 
and that is all we have to show for the energy expended. 
When a train is stopped, its kinetic energy is converted into 
heat, as the sparks which fly from the brake-shoes testify. 
Energy may be expended without being destroyed. When 
milk is spilled on the ground it is not destroyed, but it is 




Galileo Galilei. 
The Father of Experimental Science. 

Born at Pisa, 1564. Inherited from his father Vincenzio skill in music and 
mathematics, and showed talent in poetry and art. Entered University of Pisa 
at 17. His studies in hydrostatics and mechanics won for him at 24 the title of 
Modern Archimedes. Professor at Pisa at 25. Stirred up enmity by his opposition 
to Aristotle. Left Pisa and went to Padua at 28. His fame as a teacher spread 
over Europe. William Harvey was his pupil. Invented telescope, 1609. Returned 
to Pisa as Philosopher to the Duke of Tuscany, 1610. Condemned by Inquisition, 
1633. Died in 1642, the year in which Newton was born. 



L 



M 



GALILEOS EXPERIMEXT 41 

lost, because it cannot be gathered up and used. Just so 
the heat energy in the water at the base of the waterfall, or in 
the brake-shoes and the air about them, is useless because 
we cannot gather it up. The belief that energy cannot be 
created nor destroyed is called the Doctrine of the Conservation 
of Energy. This is one of the great generalizations of science, 
ranking with Newton's Law of Gravitation. The transforma- 
tions of energy form the central theme of modern physics. 

71. Perpetual Motion. For a long time inventors strove 
to produce a machine which, when once started, would go 
on forever without stopping, and do work without any 
outside assistance. We are now sure that this is impossible. 
All experience teaches that we cannot get work done without 
spending energy. Our machines must be driven by muscles, 
by wind, water, or coal, or by some other form of energy. 

FALLING BODIES. 

72. Galileo's Experiment. Aristotle taught that the speed 
of falling bodies is proportional to their weight. The proof 
that heavy bodies fall with the same speed, and the dem- 
onstration of the laws of their motion is due to Galileo. At 
the age of 25 years he was appointed professor of mathe- 
matics in the University of his native city, Pisa. He at- 
tacked the teachings of Aristotle on many points, and aroused 
bitter opposition on the part of the other professors, who 
regarded the writings of Aristotle as little less than sacred. 
The parties to the controversy agreed to a public test of the 
truth of Aristotle's statement in regard to the behavior 
of falling bodies. Two metal balls, one weighing ten times 
as much as the other, were dropped at the same instant from 
the top of the celebrated leaning tower of the city. They 
struck the ground together. 

73. This dramatic incident may be said to mark the 
beginning of modern experimental science. Much had been 
done before in various countries, but the great centres of 
learning still blindly followed Aristotle. This experiment 
called the attention of learned men to the absurdity of the old 



42 MOTION AND FORCE— WORK AND ENERGY 

doctrine, and gave a great impetus to the movement which was 
to emancipate the human intellect from slavery to authority 
in matters of science. 

74. Acceleration Due to Gravity. It has been already ex- 
plained that a constant force will produce uniform accelera- 
tion. For distances of a few hundred feet above the earth's 
surface the force of gravity diminishes so little that for 
practical purposes it may be regarded as constant. A 
mass of 1 gram is pulled toward the earth with a force of 
1 gram, and a mass of 10 grams with a force of 10 grams. 

F 

Now F = ma, or a = — . The acceleration is therefore 
m 

the same for 10 grams as for 1, since F and m have both 

been multiplied by 10. 

75. The reason why a heavy body falls no more rapidly 
than a light one may be stated in a rather more familiar form. 
Suppose several metal balls of the same size and weight 
to be dropped side by side. They will fall side by side with 
the same velocity. Now imagine a hole bored through the 
balls and a rod put through so as to make the several bodies 
into one. The speed of fall will not be increased. Four 
boys run side by side. Each uses all his strength to move 
his own body. If they hold hands they cannot run any 
faster. Four times as much force is exerted, but the body 
being moved is four times as great. 

76. Experiment shows that the acceleration due to gravity 
at sea-level at Philadelphia is almost exactly 980 cm. per 
second in one second. This is equivalent to saying that 1 
gram there equals 980 dynes. The abbreviation universally 
used for acceleration, due to gravity, is g. In this book the 
value of g will be assumed equal to 9.8 meters or 32 feet 
per second per second. A more exact value in feet is 32.2. 

77. Velocity of Falling Bodies. When a body falls from 
rest under the influence of gravity alone, its velocity at the 
end of one second is 9.8 or g meters per second; that is, 
if gravity should cease to act at the end of one second, the 
body would in the next second move 9.8 meters. When 



BODIES PRO'ECTED VERTICALLY UPWARD 



43 



gravity has acted upon the body for two seconds it will 
(being a constant force) have produced twice as much effect 
as it did in one second. The velocity at the end of two 
seconds is therefore 2 <j meters per second, and at the end 
of t seconds, gt meters. The formula v = gt, therefore, 
gives the velocity at any instant in the case of a body falling 
from rest. If t = 2^ seconds, v = 2\ X 9.8 = 21.56 meters. 

78. Space Traversed. If a body fall from rest, its velocity 
at the beginning is 0, and at the end of one second is g. The 
increase from to g has been uniform, therefore the average 



velocity is 



Multiplying the average velocity by the 



number of seconds gives the whole space traversed. For 
one second this would be 1 X \g= 4.9 meters. For the second 

second the average velocity is - — — —, therefore the space 
for the second second is \\ g = 14.7 meters. For two sec- 
onds from rest the average velocity is — <r — = g. Multi- 
plying by the time we have for the whole space covered in 
two seconds, 2g = 19.6 meters. For t seconds from rest the 



average velocity is 



+ gt 



and multiplying by the number 



of seconds, t, we have the general formula for space 
traversed in t seconds from rest, s = \ gt 2 . 

79. Bodies Projected Downward. If a body be thrown 
vertically downward with a velocity v' ', this must be added 
to the velocity due to gravity, giving for the general formula 
v = v' + gt. The average speed for t seconds would be 

V f _|_ V f _|_ gt 

~ = v' + \ gt, and the whole space traversed 

v't + \ gt 2 . That is to say, the body projected downward 
covers a space equal to the sum of the spaces due to gravity 
alone and to the projecting force alone. 

80 Bodies Projected Vertically Upward. Suppose a body 
projected upward with a velocity of 9.8 meters per second. 
This must be regarded, with respect to gravity, as a negative 
velocity, and gravity acting upon the body for one second 



44 



MOTION AND FORCE— WORK AND ENERGY 



B' C D' E' F ' 



would just suffice to neutralize the upward velocity and bring 

the body to rest. In the next second the body would fall 

to the starting point, acquiring in its fall a velocity of 9.8 

meters per second. In general, gravity takes away as much 

from the negative velocity of a body projected upward as 

it would add in the same time to the positive velocity of 

a body falling. If the upward velocity is 2g meters per 

second the body will rise for two seconds, and if it be any 

v" 
quantity v" , it will rise for - seconds. 

81. At any point in the descent, its velocity will be the 
same as the upward velocity at the same point in its rise. This 
may be shown by considering the energy involved. Suppose 
the body just starting up. Its energy is all kinetic, depend- 
ing solely on mass and velocity. When it returns, since it 
has done no external work, 1 the amount of energy must be 
the same. Being now again all 
kinetic, this energy residing in 
the same mass, must involve the 
same velocity. 

82. Bodies Projected Horizon- 
tally. Let a body be projected 
horizontally from A. Its horizon- 
tal velocity will be uniform, since 
after it starts no force acts to 
move it horizontally. Gravity 
draws it downward as if no other 
force were acting. Let B', C ', 
etc., be the positions it would 
occupy at the ends of successive 
seconds if gravity were not act- 
ing; and let B" ', C" ', etc., be 
the positions it would reach in the same times if gravity 
alone acted. At the end of one second, the body will have 

1 This is not strictly true, since the body has overcome the resistance 
of the air. For dense bodies at low velocities, this is so small that we 
may neglect it without serious error. 




Fig. 2.5. — Parabola de- 
scribed by a body projected 
horizontally. 



MODES OP DETERMINING ACCELERATION 



45 



moved over the horizontal distance AB' and also over 
the vertical distance AB" . Its actual position B is 
found by drawing the rectangle AB"BB r . In the same 
manner the points C, D, etc., are found, for the ends of 
successive seconds. In a vacuum this curve would be a 
parabola for a body projected horizontally or in any other 
direction except vertically. The resistance of the air modifies 
the shape greatly in the case of high speeds. 

83. If a gun be aimed horizontally at a target, the ball 
must always strike somewhat too low, since gravity always 
acts. If the flight of the ball occupies one second it will 
strike 4.9 meters below the point aimed at, since a body 
falls 4.9 meters in one second. The figure gives the course 
AB of a projectile of 16 meters per second initial velocity 
during one second. Then BC = 4.& meters. If the initial 
velocity be doubled, so that 
the time of flight is one-half 
second, the course AB' will 
be described in which CB' 
is only \ of 4.9 meters. It 
is evident that the deviation 




Fig. 26.— Path of projectile. 



is proportional to the square of the time of flight, and may 
be made small by increasing the speed of projection. If the 
initial speed of a rifle ball is 300 meters per second, and the 
object aimed at is 30 meters away, the time of flight is one- 
tenth of a second, and the deviation is -j-J-^- X 4.9 meters = 
4.9 cm. At long ranges guns are aimed 
considerably above the point at which 
the ball is intended to strike. 

84. Modes of Determining Acceleration. 
In investigating the laws of falling bodies, 
Galileo used an inclined plane, down which 
balls were allowed to roll. Let A repre- 
sent a body resting on an inclined plane, 
and G the force exerted upon it by gravity. Resolve this 
force into two components, F and P, parallel and perpen- 
dicular to the plane. It is evident that the force F, which 




46 



MOTION AND FORCE— WORK AND ENERGY 



urges the body down the plane, may be made any fraction 
of G that we choose, by adjusting the slope of the plane. 
Suppose F = ^V G, then the acceleration due to F will be 
-^q g, and the ball will roll slowly enough for observations 
to be taken during several seconds. The results obtained 
for spaces and velocities, multiplied by 20 will give cor- 
responding values for freely falling bodies. With properly 
arranged apparatus this method gives good results. 1 

85. Another method is that devised by Atwood, in which 
two equal masses are hung by a thread over a pulley. They 
are set in motion by another weight added to one of them, 
which may be any desired fraction of the whole mass moved, 
so that the acceleration is made the same fraction of g. 

Table of Velocity and Space Described for Freely 
Falling Bodies. 2 





Meters. 


Feet. 


a 


V 


Ss 


S 


V 


Ss 


S 


1 


9.8 


4.9 


4.9 


32 


16 


16 


2 


19.6 


14.7 


19.6 


64 


48 


64 


3 


29.4 


24.5 


44.1 


96 


80 


144 


4 


39.2 


34.3 


78.4 


128 


112 


256 


5 


49.0 


44.1 


122.5 


160 


144 


400 



a = number of seconds. 
v = velocity at the end of the second. 
Ss = space described during the second. 
S = space described from beginning. 



PROBLEMS (FALLING BODIES, ETC.). 

State results in both feet and meters where neither is 
mentioned. 

1 These results are, however, only approximate, since some of the force 
down the plane is used to cause the ball to rotate. 

2 It will be observed that columns v and Ss are arithmetic series 
whose common difference is g, and the two together taken alternately, 
16, 32, 48, etc., form a series whose common difference is £ g. 



FRICTION 47 

1. Find the space described in three seconds by a body 
falling from rest. 

2. Find the space described in the third second by a body 
falling from rest. 

3. A stone dropped from the top of a cliff strikes the bottom 
in 2.5 seconds. How high is the cliff? 

4. A body is projected vertically upward with a velocity 
of 39.2 meters per second. For how many seconds will it 
continue to rise? How many meters will it rise? In how 
many seconds will it reach the ground? 

5. A body is projected upward at an angle of 45 degrees. 
For how many seconds will it rise if its vertical velocity is 100 
feet per second? Its horizontal velocity is also 100 feet per 
second. If the ground is level at what distance from the 
starting point will it strike ? What is the initial speed in the 
direction of flight? 

6. A body is projected vertically downward with a velocity 
of 5 meters per second. How far will it move in two seconds ? 



RESISTANCE TO MOTION. 

86. Friction. In walking on bricks one is less liable to fall 
than in walking on smooth ice. We say there is friction 
between our shoes and the bricks. When two bodies are 
in contact and one or both of them move, the motion is 
hindered by the fact that they are in contact. This hin- 
drance is called friction. It is greater when the bodies are 
rough, but however smooth the surfaces may be there is 
always some friction. Sometimes friction prevenis motion. 
A concise definition is difficult to frame. 
. 87. Friction exists between two solids, between the 
particles of a solid which is bent or compressed, between 
a solid and a liquid, between two liquids, between the mole- 
cules of the same liquid, between a gas and a solid, between 
a gas and a liquid, and probably even between gases. Waves 
at sea are due to the friction between the wind and the water. 



48 



MOTION AND FORCE— WORK AND ENERGY 



a 



In order to diminish friction in the case of machinery, we 
use oil, graphite, etc., as lubricants. These fill up the 
irregularities in the surfaces, and some- 
times form a thin layer between them. 
88. Coefficient of Friction. Since 
friction hinders motion, it may coun- 
terbalance a force. ' It is therefore 
measured in the same units as force, 
and treated in general like forces. 
Suppose a force F of 100 grams is just 
able to pull a weight P of 500 grams, 
sliding on a horizontal surface. The 
ratio of moving force to force between 
F 



the 



surfaces p is called the coefficient 



Fig. 28.— A method 
of measuring coefficient 
of friction. 



the coefficient is -J. 



of friction. In the case supposed, 

89. Laws of Friction. Experiment shows that friction 
between two solids is (1) proportional to the force between 
the surfaces; (2) independent of the area in contact; (3) greater 
at starting than after motion has begun, and, at least in the case 
of metals, (4) less between smooth surfaces of different sub- 
stances than between those of the same substance. The first 
and second of these are shown by using as in Fig. 28 a rec- 
tangular block whose width is twice its thickness, and placing 
it first on one face and then on the other. If the two faces 
are equally smooth, the force required to draw it will be 
found to be the same. If a load be placed upon the block 
equal in weight to the block, the force required will be twice 
as great. The third law may be conveniently shown by 
drawing the block with a spring balance. The reading will 
be higher at the start than after the block begins to slide. 
The force required to start it measures what we may call 
starting friction, and that required to keep it going sliding 
friction. 

90. Because of the fact expressed in (4) the bearings in 
which the axles of heavy machinery turn are made of a 
metal different from the axles. It is supposed that when 



RESISTAXCE OF THE AIR 



49 




Fig. 29. — Diagram of 
ball-bearing. 



two smooth surfaces are of the same metal, the molecules 
of one fit into the spaces in the other to a greater extent than 
when the molecules are of different 
sizes, thus causing more resistance 
to motion in the former case. 

91. When an object rolls over a 
surface, friction is also experienced. 
Rolling friction is, in general, much 
less than sliding. Ball bearings are 
used in certain kinds of machinery 
because, to a large extent, they sub- 
stitute rolling for sliding friction. 

The diagram illustrates how a ball bearing works. As the 
axle A rotates in the bearing B, the smooth steel balls C 
roll around between journal and bear- 
ing, the ring of balls revolving once in 
B for about two revolutions of A. 

92. Resistance of the Air. It has 
already been mentioned that the inertia 
of the air makes it unable to escape 
from a sudden blow. A parachute falls 
slowly even with a heavy weight, be- 
cause of the inertia of the air which 
must escape from under it. The flight 
of a bird is made possible in the same 
way, but the flight of thistle-down is 
due to a different cause. In this case it is not chiefly the 
inertia of the air, but its friction against the threads of the 
down which retards the fall. This fric- 
tion increases with the area of the sur- 
face. The pressure here is not the 
weight of the object, but the pressure 
of the atmosphere against it. This is 
about 1 kilogram per cm. 2 and of course Fig. 31.— Thistle seed, 
the greater the area the greater the 

total pressure, and, consequently, the greater will be the 
friction. 
4 




Fig. 30. — Parachute. 



50 MOTION AND FORCE— WORK AND ENERGY 

93. In the parachute case friction is a very small factor. 
In the case of the thistle-down the inertia of the air 
is a very small factor, because the air is pushed aside so 
slowly and for such a small distance. Sixteen hands 
grasping a rope hold it with sixteen times as much force 
as one. So the friction of the air against the many long 
threads of the down hold it against the small force 
exerted by gravity. Spider threads, if the air is stirring 
a little, will float long distances. " Ballooning" spiders 
are actually carried by the friction of the air against a 
long thread which they have sent out and which the air 
has carried up. 

94. Dust made of very small particles of matter far denser 
than spider web floats in the air for a long time. The 
particles have not very extended surfaces, but the surface 
of a particle becomes smaller less rapidly than the weight, 
with diminishing diameter. If a body be broken into pieces 
whose diameter is -fa as great as before, the surface of each 
becomes T fa and the volume and weight each 10 1 00 of what 
they had been. Since the friction of the air against the 
particles is proportional to their area, it is clear that friction 
is greater in proportion to the pull of gravity in the case of 
the smaller particles. 

95. The inertia of the air also plays here an important 
part. The resistance due to this cause increases with the 
square of the velocity of the moving body. This may be 
roughly explained by stating that a body moving with twice 
as much speed as another of the same size strikes twice as 
many molecules of air in a given time, and strikes each 
twice as hard. Suppose a small body beginning to fall: 
its speed increases, but the work done in pushing the air 
aside increases as the square of the speed. If, then, the body 
fall long enough the resisting force will increase until it equals 
the pull of gravity, and no further acceleration will be 
possible, but the body will float down with uniform speed. 
This is what happens to ants falling from trees, to rain-drops, 
and to snow-flakes. 






POTENTIAL ENERGY 51 

96. The large drops of a thunder-shower fall far more 
rapidly than smaller drops. Very fine dust particles fall so 
slowly that their descent is sometimes scarcely observable, 
and a very small motion of the air suffices to keep them 
in suspension indefinitely. Such bodies as nuts from trees 
or stones from balloons do not reach their limiting speed 
before reaching the earth. Aeronauts, therefore, do not 
throw out stone ballast, but fine sand which floats 
down. 

97. "Shooting stars" are often observed to move more 
slowly in the latter part of their flight. They are small 
objects which, falling toward the earth from outer space, 
strike the atmosphere with such high velocity that the 
resistance developed heats them white hot. They generally 
burn up or are worn into infinitely small fragments in a 
second or two. 

98. Bodies Moving in Water. The same conditions which 
have been discussed in the case of the air, obtain in greater 
degree for objects falling in water. Quite large pebbles 
reach their limiting velocity in a few meters, and fine mud 
requires days to settle a single meter in still water. In 
the case of steamships, most of the energy used is expended 
in pushing the water aside. To drive a vessel twice as fast 
takes approximately four times as much coal. 



FORMULA FOR ENERGY. 

99. Potential Energy. When a body has been lifted through 
a distance s centimeters, the work done on it is the product 
of its weight in grams by the number of centimeters through 
which it was lifted. This product would be gram-centi- 
meters. In order to reduce it to absolute units we must 
multiply by g, the number of dynes in 1 gram. If m = 
the mass in grams, mg = the weight, and mgs = the potential 
energy of the body at a height s, because mgs ergs of work 
have been done in lifting it to that height. 



52 MOTION AND FORCE— WORK AND ENERGY 

100. Kinetic Energy. Now suppose the body to fall 
through the distance s. The potential energy would be 
transformed without loss into kinetic. We wish to express 
this in terms of mass and velocity. In the expression mgs, 
substitute for s its value J gt 2 , and we have for the total 
energy \ mg 2 t 2 . But v = gt, therefore, g 2 t 2 = v 2 , and the 
kinetic energy of a body of mass m and velocity v is J mv 2 . 

101. Energy of Rotation. The kinetic energy of a rotating 
body whose moment of inertia is K and angular velocity 
co is J Kco 2 . Here co is the speed in centimeters per second 
of a particle 1 cm. from the centre. 



THE PENDULUM. 

.102. Simple Pendulum. The ideal simple pendulum should 
have a ball with mass, but no size, suspended to an im- 
movable support by a weightless and perfectly flexible 
thread. These conditions are so nearly realized as to give 
practically perfect results if we use a ball of metal weighing 
100 grams or more, suspended to a firm support by a fine 
thread of cotton or silk. When the ball is drawn aside and 
released it returns to its equilibrium position under the 
influence of gravity. Inertia carries it past this position, and 
if no work were done in overcoming the resistance of the air, 
and the stiffness of the thread, it would swing just as far 
beyond the middle point as it had been drawn aside from it. 
It would then swing back to the starting point, and this 
process would be repeated indefinitely. In practice each 
swing is a little shorter than the preceding one, and the 
energy is finally all dissipated as heat. 

103. Periodic Motion. When a body travels over a certain 
path again and again, each journey taking the same time, 
the motion is called periodic. The periodic time is the time 
required to make a complete cycle. For the pendulum 
the cycle is called a complete vibration, and includes two 
swings. In one swing the "bob" moves from A to C. When 



FIRST LAW 



53 




it has come back to A, the cycle is complete. The discovery 

that the swings of a pendulum are made in equal times 

was made by Galileo, at the age of 17. 

He observed the chandelier swinging in 

the Cathedral at Pisa, and judged by 

counting his pulse that the time of swing 

was uniform. 

104. Energy of Pendulum. When the 
bob is held at A, Fig. 32, it has poten- 
tial energy due to the height PB. This 
is transformed into kinetic, and as the 
bob passes through the middle position 
its energy is all kinetic. From B to 
C the reverse transformation takes 
place, and so on, twice in every swing the energy passes 
from one form to the other. 

105. Seconds Pendulum. If such a pendulum as has been 
described be made 99.3 cm. long from the point of support 
to the centre of the bob, then drawn aside 5 cm. and released, 
it will make 60 swings in one minute. The distance from 
the point of support to the " centre of oscillation," which, 
in a pendulum of this kind, is practically at the centre of 
gravity of the bob, is called the length of the pendulum. If 
the length be made more or less than 
99.3 cm., the time of one swing will 
be more or less than one second. 

106. First Law. If, however, with- 
out changing its length, the pendulum 
be made to swing through arcs 5, 10, 
and 20 cm. long, the time of swing 
will be one second in each case. The 
angular distance to which the pendu- 
lum swings on each side of its position 
of equilibrium is called its amplitude. 

The time of swing of a pendulum is independent of the ampli- 
tude if the amplitude be small. Even if the bob be drawn 
aside 30 cm., the time will be so nearly the same as before 




-^-<L- 



54 MOTION AND FORCE— WORK AND ENERGY 

that we cannot note any difference in observing 60 swings. 
When the bob is released at the greater distance, as A, Fig. 33, 
it starts down a steeper slope than if it started at A' ', and so 
moves more rapidly than if it had a less amplitude and 
accomplishes its journey in the same time. 

107. Second Law. The times of pendulums at the same place 
are proportional to the square roots of their lengths. If three pen- 
dulums are arranged, having lengths of 99.3 cm., ^ X 99.3 cm., 
and J X 99.3 cm., the number of swings in one minute will be 
found to be 60, 90, and 120 respectively. Their times will be 1 
second, f second, and \ second. The converse of the second 
law is often convenient. The lengths of pendulums at the same 
place are proportional to the squares of their times. A pen- 
dulum to make one swing in 2 seconds must be 397.2 cm. long, 
and if the time is to be 3 seconds it must be 9 X 99.3 cm. 

108. Third Law. If a pendulum having an iron bob be so 
arranged as to swing just above the pole of a strong magnet, 
it will be found to vibrate more rapidly than it does with 
the magnet removed. This is because increase of force 
causes more rapid motion, and therefore a swing is accom- 
plished in less time. The rate of vibration of a pendulum 
is therefore slower in Guiana than would be that of the same 
pendulum at Paris, because Paris is nearer the centre of the 
earth, and the force of gravity is greater there. The time 
of swing of the same pendulum at different places is inversely 
proportional to the square root of the intensity of gravity. 

109. Effect of Varying Mass and Material. The mass of the bob 
does not affect the time. This is for the same reason already 
stated in the case of falling bodies. The material of the bob 
also has no effect on the time. Newton concluded from this 
fact that the earth attracts all kinds of matter equally. 

110. Formula for Pendulum. All of these laws are included 

in the formula t = n — * where t is time of one swing 

9 
1 A mathematical demonstration of this formula is too difficult for this 
book, but the value of the formula is so great that the student is asked 
to accept both it and the laws as resting on experimental evidence. 



M 



CLOCK PENDULUM 



55 



in seconds, n is the ratio of the circumference of a circle 
to its diameter, I is the length, and g is the acceleration due 
to gravity. 

111. Since the value of t does not include either mass, 
amplitude, or material, it does not depend on them. If g 
be a constant, as it is at a given place, we may write the 

formula t = -7= X V I , and read it t = the square root of 

V 9 
the length multiplied by a constant, or t varies as the square 

root of I. In like manner, if I be constant, t varies inversely 

as the square root of g. 

112. This formula enables us to compute the value of g, 
since the time and length of a pendulum can be measured 
with great accuracy: 

2 l ^ l 

t 2 = t: 2 — ; a = -a-. 



Similarly if g and t be given, I may be computed. 

113. Compound Pendulum. If a bar (Fig. 34) be suspended 
in such a manner as to vibrate about a point of support A, 
particles of the bar b, b' ', b" , at different distances 
from A tend to vibrate in different times. But 
because the bar is rigid, they are obliged to vibrate 
in the same time. The result is a compromise. The 
length of the pendulum is the distance from the 
point of support, not to the centre of gravity of 
the pendulum, but to the particle in the axis of the 
bar whose natural period is the same as that of 
the bar as a whole. This point is called the centre 
of oscillation. For a uniform rod suspended at its 
upper end, this point is about one-third of the length 
from the lower end. All pendulums having metal 
rods and large bobs are compound pendulums, and 
their length is considerably greater than that of the equiva- 
lent single pendulum. 

114. Clock Pendulum. Since a pendulum of fixed length 
at a given place vibrates always in the same time, it may 



ti 



Fig. 34 



56 



MOTION AND FORCE— WORK AND ENERGY 



be used to measure time. It is only necessary to connect 
with it a device to count the swings and to give it a little 
push each time it swings, to keep it from stopping, and we 
have a pendulum clock. The push is given by the escapement, 
so called because one tooth of the 
wheel escapes for every complete 
vibration of the pendulum. The 
counting is done by a train of 
wheels connected with the escape- 
ment wheel, and by the hands and 
face. The energy is supplied by a 
coiled spring or a raised weight. 
Methods of preventing changes of 
length of the pendulum due to 
changes of temperature . will be 
described in the chapter on Heat. 



ELEMENTARY MACHINES. 

Fig. 35. — Clock escape- 

-t i r a ■»*■!-• • xi • i_ ment. (The position of the 

115. A Machine is a thing by ■. , , . , 

. . , . ,. , . ,, n . pendulum rod is shown by 

which energy is applied to the doing dotted lineg } 

of work. Complex machines may 

be resolved into a few simple elements. These have been 

commonly called the mechanical powers, and their number 

given as six: lever, pulley, wheel and axle, inclined plane, 

wedge, and screw. To these the cord is often added, and 

the cam and various other j R (7 

devices may fairly be con- 

sidered separate elements. 

116. The Lever, in its 
simple form is a rigid bar 
supported on an edge 
called the fulcrum. The two forces have been called 




z — 

R 

Fig. 36.— Straight lever. 



the power and the weight, since the lever is often used 
to lift heavy weights, and the acting force was called the 
power. Since this use conflicts with the sense in which 



THE WHEEL AND AXLE 



57 



power is now used (paragraph 69), we shall use the terms 
force and weight or simply call them both forces. In 
Fig. 36 the forces F t and F 2 are held in equilibrium by the 
resistance at the fulcrum R. The three are parallel forces 
in equilibrium, and it is evident that the force at R is equal 
and opposite to the sum of F x and F 2 , which must in turn have 
equal and opposite moments. Their moments are opposite 
because they tend to produce rotation in opposite directions. 
It is evident that the forces are inversely proportional to 
their lever arms, so that if AB (Fig. 36) is twice as long as 
BC, F t will hold in equilibrium a force twice as great as itself. 
117. Leverage. The ratio of the arms is called the leverage 
of the lever, thus in Fig. 37 the force is acting with a leverage 






3 



B 



m 



Fig. 37 



Fig. 38 



of 3J to support TT, if RB = 2 and RF = 7, since RF -=- 
RB = \ = 3J. In Fig. 38 the leverage is J. 

118. Law of the Lever. When the lever is in equilibrium 
the moments of the two forces are equal and opposite, or the 
forces are inversely proportional to their lever arms. 

119. The Wheel and Axle, shown 
in diagram in Fig. 39, is really a 
continuous lever. Its equilibrium 
conditions are precisely the same 
as for the lever, the axis of rotation 
of the wheel taking the place of the 
fulcrum as a centre of moments. 
The lever arm of the force is OB, 
the radius of the wheel, and that 
of the weight OA, the radius of the 

axle. Since the circumferences of circles are to each other 
as their radii, we may also say F: W: : the circumference of 
the axle : circumference of wheel. 




Fig. 39.— Wheel and axle. 



58 



MOTION AND FORCE— WORK AND ENERGY 



120. Train of Wheels. When, as in a train of wheels, 
the circumferences are furnished with cogs, the number of 
cogs is taken instead of the circumference. The train of 
wheels in a watch enables the spring, by making a few turns, 
to drive the second hand through more than a thousand 
revolutions. In the 
train of wheels used 
on a hand-power der- 
rick, the effect is to 
give to the force ap- 
plied at F in Fig. 40 
a great leverage in 
its pull on the rope 
R. Suppose A and 
B each to have 12 
cogs, and D and E 

each 60. Let the crank P be 20 cm. long and the radius 
of C be 5 cm. It will require 5 revolutions of B to cause 1 
revolution of E and C, and 5 of A to cause 1 of B and D. 
Therefore, 25 revolutions of A will cause 1 revolution of C. 
The ratio of the length of the crank to the radius of C being 
20 : 5 or 4, we have as the leverage of the force exerted at 




Fig. 40. — Train of wheels. 



F, 4 X 25 



100. 



121. With such apparatus, or any except the most simple, 
the expression mechanical advantage 1 is used instead of 
leverage. * With the apparatus of Fig. 40 a force of 10 kg. 
applied at F will hold in equilibrium a pull of 1000 kg. on the 
rope. In order to wind up the rope against such a pull, 
there must be added to the 10 kg. at F enough force to 

1 Some writers use the expression "velocity-ratio" as a substitute 
for the older term mechanical advantage. It means simply the ratio 
of the velocity of the weight to that of the force, and is not concerned 
at all with friction. It is also the ratio of displacements, and is the 
inverse of the ratio of the forces. The words mechanical advantage 
are liable to mislead the student by suggesting a possible advantage 
in the matter of work done. This objection does not apply to velocity- 
ratio. 



COMBINATIONS OF PULLEYS 



59 



X 



£££ 



® 

Fig. 41. — Fixed pulley. 



^ 



v; 



D 



overcome the friction of the machine, and then an additional 
quantity to produce an acceleration. 

122. The Pulley is also a con- 
tinuous lever, whose arms are equal 
or in the ratio of 2 : 1. A pulley 
fixed to an immovable support will 
be in equilibrium in the conditions 
of the figure when the weights 
attached to the cord are equal, 
since the lever arms AC and BC 
are equal. In Fig. 42 the cord is 
attached at D to a fixed support 

and pulled by a force F. In this case the fulcrum of the 
lever is B, the lever arm of W is CB, and of F, AB or 

2CB. Therefore, by the law of the j~ -j 

lever W = 2F when the system is 
in equilibrium. Of course W in- 
cludes the weight of the pulley. 

123. Another view of the movable 
pulley considers the three parallel 
forces, F, W, and the pull on the 
cord BD. Since the system is in 
equilibrium, W is equal to the other 
two. F = the force along BD be- 
cause AC = CB, therefore W = 2F. 

124. Combinations of Pulleys are often used. Several are 
shown in Fig. 43. In I the pull on a is \ W; but P = 
pull on a, therefore, P = \ W. In II the arrangement is 
the same, except that the rope is fastened to the frame 
holding the pulley. The conditions are not precisely the 
same, since the branches of the rope are not exactly parallel, 
but the difference is negligible. If P took the direction P' f 
its value would be unchanged, since its lever- arm AC is the 
same length as before. In III the pulley m equalizes the 
pull on a and b; n equalizes that on a and c. Therefore the 
pull on b is J W and P = \W , since the pulley o equalizes 
b and P. With a combination of pulleys having one rope, 



Fig. 42. — Movable pulley. 



60 



MOTION AND FORCE— WORK AND ENERGY 



the ratio of weight to force equals the number of branches 
of rope supporting the weight, when the system is in equilibrium. 





125. It is customary to place the pulleys which are fastened 
together, as o and n (Fig. 43), side by side on a common axis, 
supported in a frame called a block. 
In order to raise a weight, the same 
additions must be made to P as in the 
case of the wheel and axle, to over- 
come friction and cause acceleration. 

126. Inclined Plane. In loading 
barrels into a wagon, they are some- 
times rolled up a pair of "skids." 

The force which pushes the barrel p IG 44 Double pulley 

up the plane is less than the weight 
of the barrel. In Fig. 45 let 
G represent the weight of 
the barrel and its centre 
of gravity. Resolve G into 
components, F' parallel to 
the plane and P perpen- 
dicular to it. Now F' urges 
the barrel down the plane, 
so an equal and opposite 
force F will support it. From Fig. 45.— Inclined plane. 



block. 




THE SCREW 61 

OF 1 ' P Ti 
the similar triangles OF'G and CBA, qq = -jt^. That is, 

a /ore? acting parallel to an inclined plane will support a load 
as many times greater than itself as the length of the plane is 
greater than the height. 

127. Another demonstration of this law considers the 
energy expended while the force is in action. In order to 
raise the weight a distance BC against gravity, the force 
F must act through a distance AC. Disregarding friction 
and the added force necessary to cause motion up the plane, 
both of which in such a case are relatively small, we have 
F X AC = G X BC. That is to say, the work done by the 
force equals the work done on the weight. Converting the 
equation into a proportion, F : G : : BC : AC, or using the 
initials of Force, Weight, Height, and Length, F : W: : H : L. 

The most familiar instance of the inclined plane is a hill 
in a road or a "grade" on a railroad. The steeper the grade 
the fewer cars the locomotive can pull. 

128. The Wedge is simply an inclined plane which moves. 
It is used in splitting wood and rocks and for various other 
purposes where it is necessary to exert great force through 
small space. All "edge tools" are wedges, whether called so 
or not. The mathematics of the wedge is similar to that of 
the inclined plane, but more complex because 
the force being overcome usually consists of 
two parts whose directions are not parallel. 

129. The Screw may be typified by an 
inclined plane wound around a cylinder, as 
shown in Fig. 46. It is used in a multitude 
of forms for holding the parts of machines F g 46 
and other things together, for raising weights 
and producing pressure. The projecting part a (Fig. 48) 
which winds spirally around the body of the screw is called 
the thread, and the distance from a to a', the distance 
between the threads, is called the pitch of the screw. 

130. In the case of a screw driven into wood, the thread 
moulds the wood into an inside screw. If there is a separate 




62 



MOTION AND FORCE— WORK AND ENERGY 



piece of metal having a hole with a thread to fit the screw, 
this piece of metal is called & nut, and the whole is a bolt. 
If by turning the screw in a clockwise direction it retreats 
from the observer, it is called a right-hand screw, but if it 





Fig. 47.— Right-hand 
screw. 



Fig. 48.— Left-hand 
screw. 



M 



Fig. 49.— Bolt. 



approaches, it is a left-hand screw. Fig. 47 is a right- 
hand and Fig. 48 a left-hand screw. The nuts which keep 
the wheels of a carriage in place are right-hand on one 
side of the carriage and left-hand on the other. Since 
nearly all screws are right-hand, we 
usually omit the adjective in that 
case. 

131. The law of the screw may be 
well illustrated by the lifting-jack, 
shown in Fig. 50. While the end of 
the lever A describes a revolution, the 
screw rises the distance between the 
threads. Disregarding friction, the 
work done in the two cases is equal, 

and we have F : W : : distance between the threads 1 : cir- 
cumference described by the force. 

132. Sliding friction between screw and nut is an im- 
portant factor. When a wood-screw is driven into place, 
friction holds it there. A vise is screwed up to hold a piece 
of work, and it stays in place because of friction. The 

1 Screws are sometimes made with two threads. In this case we must 
say "distance between two consecutive turns of the same thread." 




Fig. 50. — Jack screw. 



DEFINITIONS 63 

extra energy which we must use in driving the screw is com- 
pensated for by the factor of convenience. A lifting-jack 
is often more convenient than a lever, because it can be used 
in a smaller space. 

133. The Cord used with the wheel and axle and pulley, 
is a very necessary help, serving to change the direction of 
a force, and to transmit a pull to a distance. All the other 
" mechanical powers" may be reduced to two, as has been 
shown, the lever and the inclined plane. 

134. The General Law of Machines is, the work done by the 
force is equal to the work done on the weight. This disregards 
the energy dissipated into heat on account of friction, 
but takes account of the excess on the part of the power 
which is expended in producing motion. The work done 
by this excess is found as kinetic energy in the moving 
system. 

135. Efficiency of a Machine. In every machine some of 
the energy expended in driving it is used in overcoming 
wasteful resistances, and so does no useful work. In the 
lever the proportion of energy so wasted is small; in the 
screw it is large. This difference is expressed by saying 
that the lever is more efficient than the screw. The ratio 
of useful work done to the total energy expended is called the 
efficiency of the machine. In some machines this ratio is 
as high as .95, but can never be 1. 

136. Definitions. The subjects discussed in this chapter 
are included in the general term mechanics, which is one of 
the most important departments of applied mathematics. 
Mechanics is variously subdivided. Kinematics (Greek 
kinema, motion) treats of motion, statics (Latin sto, stand) 
of forces in equilibrium, and dynamics of forces at work. In 
the brief treatment of the mechanics of solids in this book, 
the several departments have not been treated entirely 
apart from each other. Much of our work in regard to liquids 
and gases will deal with the mechanics of those bodies. 



64 MOTION AND FORCE— WORK AND ENERGY 



EXERCISES AND PROBLEMS. 

1. A boat is rowed directly across a stream at the rate of 
4 miles an hour. The current has a speed of 3 miles an hour. 
What is the resultant velocity of the boat? 

2. A uniform straight lever five feet long weighs 4 lbs. 
A weight of 1 lb. is hung at one end and 20 lbs. at the other. 
A third weight of 15 lbs. is hung one foot from the 1 lb. 
Where must the fulcrum be placed that the lever may 
balance? (paragraph 52). 

3. If 30.48 cm. = 1 foot, 980 dynes = 1 gram, and 453.6 
grams = 1 lb., find the number of ergs in 1 foot-pound. 

4. What kind of energy has a horse (a) in the stable? 
(b) Trotting along the road? 

5. A mill is driven by water-power. Trace back the energy 
as far as you can. Trace also the energy of the horse. 

6. A gun is fired at a target 1000 feet away. The bullet 
starts with a speed of 2000 feet per second. Disregarding 
the resistance of the air, how high above the target must 
the gun be aimed ? Will the actual aim be higher or lower ? 
Why? 

7. Are ball bearings used in light or heavy machinery? 
Give reasons. 

8. If the coefficient of friction between the surfaces be .32, 
what force would be required to push along the floor a 
box of groceries weighing 100 lbs? 

9. What is smoke? Why does it rise? What becomes 
of it? 

10. A bullet weighing 15 grams is moving with a velocity 
of 600 meters per second. How many ergs of kinetic energy 
has it? 

11. A hammer weighing 500 grams moves with a velocity 
of 20 meters per second. What is the energy of the blow 
in ergs? In foot-pounds? 

12. What will be the time of swing of a pendulum whose 
length is 60 cm., if g = 980 cm. per second per second? 



EXERCISES AND PROBLEMS 65 

Solution: — Using the formula t = tz — , we have t = 
__ 9 

* V ^ =?r ] l=^x| ]/3 = .7773 second. 
980 49 7 

13. With the same value of g, find the time of a pendulum 
2 meters long. 

14. How long is a pendulum that swings once in J second? 
(g = 980 cm.). 

15. What is the value of g at a place where a pendulum 
2 meters long swings once in 1.42 seconds? 

16. A force of 10 kg. applied to a lever supports 60 kg. 
placed 20 cm. from the fulcrum. What is the lever arm of 
the force ? 

17. A. and B. carry a weight of 240 lbs. hung between 
them on a bar 3 feet long. If A. carries 80 lbs., where is the 
weight hung ? 

18. An object weighed with correct weights on a false 
balance appeared to weigh 10 grams when placed in one 
pan, and 14.4 grams when placed in the other. What was 
its true weight? 

19. In another case the apparent weights were 100 grams 
and 121 grams. What was the true weight? Find also the 
ratio of the lengths of the balance arms. 

20. In IV, Fig. 43, p. 60, a force of 5 lbs. at P holds the 
system in equilibrium. What is the combined weight of 
W and the movable block? 

21. A boy can push with a force of 100 lbs. He has to 
roll a barrel of sugar weighing 400 lbs. into a wagon 3 ft. 
high. How long must the skids be? 

22. The slope of a hill is 264 ft. to the mile. Disregarding 
friction, what force will hold in equilibrium on the hill a 
wagon which with its load weighs 3000 lbs. ? 

23. In a certain steam engine, four-fifths of the energy 
of the coal used passes into the air as heat, carried by the 
steam and by the smoke and gaseous products of combus- 
tion. Five per cent, of the energy is used in overcoming 
friction. What is the efficiency of the machine? 

5 



CHAPTEE III. 

LIQUIDS. 

137. Three States of Matter. In solids the molecules 
keep their places with respect to one another, held by the 
little-understood force which we call cohesion. In liquids 
cohesion is in general less than in solids, and the molecules 
move about among each other more or less freely. In gases 
the molecules repel each other, the force of cohesion being 
so far overbalanced that it seems to any but the most minute 
observation to be absent. The force which tends to drive 
the molecules apart is due to heat. In solids it is small 
compared to cohesion. In typical liquids the two are nearly 
balanced, and in gases the repellent force is much more 
apparent. Solids keep their volume and shape ; liquids keep 
their volume, but take the shape of the vessel in which they 
are contained; gases expand indefinitely, having neither 
definite shape nor definite volume. Liquids and gases are 
also called fluids (Latin fluo, flow). 

138. Liquids and solids are not always sharply defined. 
While the molecules of water move about among each other 
with great freedom, syrup has much greater cohesion and 
flows slowly. Such liquids are said to be viscous. Pitch 
is so viscous at 22° C. as to seem like a solid. If a cubical 
piece of it be placed on a flat surface, and the temperature 
kept at about 22° for a week, it will spread out (that is, flow) 
over a space several times as large as it at first covered. 
At a temperature somewhat lower it becomes a true solid, 
and at 50° it flows quite freely. A solution of gelatin in 
four times its weight of hot water, on being allowed to cool, 
passes by degrees into a solid state, and at 20°, although 
not at all hard, is a definite solid — a jelly. A piece of soft 

(66) 




MOLECULES OF LIQUIDS IN MOTION 67 

rubber is a true solid, although far softer than some liquids 
with high viscosity. Water is, of course, the typical liquid, 
and we often say water instead of u a, liquid" in discussing 
the properties of liquids. 

139. Comparison of Liquids with Finely Divided Solids. 
Flour, lycopodium powder, and plaster of Paris flow much 
like liquids. So do solids in larger pieces, if the pieces are 
smooth and rounded, as in the case of wheat, clover seed, 
shot, or dry sea-sand. If a quantity of wheat be poured 
into a large vessel, it will lie heaped up on the side where it 
was poured in. The slope will not be 
very steep, but so long as the vessel is 
undisturbed, the surface will not be level. 
Consider three objects arranged as in 
Fig. 51. The weight G of the particle a 
is resolved into two forces, a b and a c. 
Each of these is further resolved into 
two; one horizontal and one vertical. 

The sum of the vertical components is G; that is to say, 
the objects b and c bear upon the plane M N with a force 
equal to the sum of the weights of all three. The horizontal 
components d and e tend to force b and c apart, and if the 
friction be not too great they will push them apart. A 
number of spherical objects piled on a level surface would, 
therefore, if friction were not acting, spread out so that all 
the objects would rest on the plane. 

140. Similarly it may be shown that under the same condi- 
tions, spherical objects placed in a vessel would arrange 
themselves so that the upper surface presented by the mass 
of bodies would be level. But all solid bodies have friction 
against each other, which neutralizes a part of the horizontal 
component, and so the objects remain heaped up so long as 
they are undisturbed. 

141. Molecules of Liquids in Motion. If, now, our measure 
of wheat be jostled, the heap will subside and the surface 
become almost perfectly level. This suggests the reason 
why mobile liquids at rest have a level free surface. The 



68 



LIQUIDS 




Fig. 52 



internal friction of such substances is less than that of any 
group of rounded solids; but, however small it may be, this 
friction would prevent the force of gravity from rendering 
the surface perfectly level if it were not for the very small 
vibratory motions of the molecules among each other. One 
evidence out of many in support of this kinetic theory of 
liquids is found in the fact of evaporation at temperatures 
below the boiling point. (See paragraph 482.) 

142. Free Surface of Liquids. In general, the free surface 
of a liquid means that part in contact with the air, and when 
the liquid is at rest, this surface, as has been already men- 
tioned, is level. Here, again, is a word which we all under- 
stand, but of which it is difficult to give a precise definition. 
If the earth were spherical, that is, if it 
did not rotate on its axis, every part of a 
still water surface would be at the same 
distance from the earth's centre. Approxi- 
mately, then, a level surface is one every 
part of which is equally distant from the 
earth 7 s centre. 1 If a surface of water has been disturbed 
so as to have a slope, as in the figure, gravity acting on a 
particle at A produces a component AB, parallel to the 
surface, which causes it to slide down, and so the higher 
molecules slide down and fill up the depression, and the 
surface becomes level. 

143. Spirit Level. If a very slightly curved tube of glass 
be nearly filled with alcohol and sealed, the bubble of air 
which remains will 
lie at the highest 
part of the tube. 
Such a tube fast- 
ened to a piece of 
wood or metal having a straight edge, and so adjusted that 
when the edge is level the bubble is in the middle of the 

1 A level surface may be defined as one such that equal work would be 
required to carry a given mass from the earth's centre to any part of 
the surface. 




Fig. 53.— Spirit level. 



COMMUNICATING VESSELS 



69 




Fig. 54 



visible part of the tube, is called a spirit level. It is of 
great use to builders and surveyors. 

144. Curvature of the Earth. A small water surface is 
very nearly plane, but if the extent is several miles, the 
deviation is easily seen. In one 

mile the surface falls away from 
a tangent line 8 inches. At two 
miles from the point of tangency, 
the tangent and the surface are 
32 inches apart, and in general 8 

inches multiplied by the square of the number of miles gives 
the deviation at that distance. In Fig. 54 the distances are, 
of course, entirely out of proportion, but 
the three horizontal distances are equal, 
and the vertical distances are in the pro- 
portion 1:4 : 9. 

145. It is shown in Plane Geometry 
that if AB be tangent to the circle of 
Fig. 55 at B, and AC be a secant, inter- 
secting the circumference at 0, AB is a 
mean proportional between AO and AC. 
So long as A B is a few miles only, AC is to 
all intents and purposes the diameter of 
AC = D, considered constant, and AO = h. 

(AB) 2 




Fig. 55 

the earth. Let 
Now h : AB : : 



AB : D, or h = 
mile, then h 



D 



D is about 7920 miles. Let AB = 1 



8 inches. If AB = 2 miles, 



h is WW of a mile, and h varies as (AB) 2 



■ — B — I 



TWO °f a mne 

TWO 

146. Communicating 

Vessels. If the sur- 
face of a liquid be 
interrupted, as at A, 
Fig. 56, the remaining 
part of the surface is 
still level. This is 
true however great the interruption, if the liquid is at rest, 
as in the communicating vessels of Fig. 57. If a reservoir 



Fig. 56 



Fig. 57 



70 LIQUIDS 

be placed at a height and pipes laid from it to houses on 
lower ground, the water can rise in the houses (when no 
faucets are open) as high as the surface of the water in the 
reservoir. 

147. Surface Tension. A very small quantity of water 
on a wax surface forms into a globular drop. Rain falls in 
drops. Mercury spilled on a table forms into drops. If 
you chase a globule of mercury around with a finger or 
pencil point, it behaves precisely as if it was enclosed 
in a thin rubber membrane. It is, in fact, enclosed in a 
marvellous elastic self-healing surface film of considerable 
strength. 

If air be forced into a thin rubber bag of irregular shape, 
it is distended, and because the contractile force of the 
rubber tends to make it as small as possible, the smallest 
surface which can contain a given volume being spherical, 
the rubber membrane becomes a sphere. Toy balloons 
are familiar examples. For the same reason the drops of 
dew which hang on the grass and leaves are spherical, because 
the water is contained within an elastic film. The contractile 
force exerted by the film gives occasion for the name, sur- 
face tension. Pure water has a greater surface tension 
than most liquids. That of mercury, however, is nearly 
7 times as great. Surface tension diminishes with rise of 
temperature, being dependent on the force of cohesion in 
the liquid. 

148. Formation of Drops. When water is flowing under 
slight pressure from a very small opening, as shown on an 
enlarged scale in the diagram Fig. 58, the surface film shown 
over the opening in 1 is gradually 
distended by the water pouring into 
it until finally the weight of water is 
so great that the film is broken and 
the drop falls, the film healing at the FlG 58 
point of rupture, and then the process 
is repeated. It is clear that in mobile liquids the size of the 
drop will depend on the density and the surface tension, all 




CAPILLARY TUBES 



71 



Fig. 59 



A 



drops of the same liquid formed without disturbance at the 
same temperature being of the same size. Water forms 
larger drops than alcohol, having a higher surface 
tension in proportion to its density. 

149. A small stream of water falling vertically 
often breaks into drops at a nearly constant point. 
As the water falls its velocity increases and the 
stream narrows. When the diameter becomes some- 
what less than that of a drop, an unstable condition 
is reached and the stream breaks into drops which 
fall separately. Often the rippled condition above 
the breaking point can be clearly seen (Fig. 59). 

150. Capillarity. Some liquids, as oil and alcohol, mix 
freely in all proportions. Others, as water and most oils, 
seem not to mix at all. Similar differences are observed in 
the behavior of liquids toward solids. Water 
adheres to clean glass or metal, but not to 
paraffin or an oiled surface. Little is known — 
in regard to the cause of these differences. 
When a glass is partly filled with water, the 
surface turns up at the edge where it meets Fig. 60 

the glass. The diagram (Fig. 60) is an 
enlarged cross-section. The liquid tends to spread on the 
glass, and so draws the edge of the surface film up to A. It 
stops creeping up when the force exerted by the film is just 
sufficient to support the weight of water in the space ABC. 

151. A glass vessel of mercury, on the 
contrary, has a surface which is convex up- 

ward instead of concave- Here the liquid £ 

does not wet the glass, and so seems to be 

repelled by it. The forces are in equilibrium 

when the total strength of the film is equal Fig. 61 

to the weight of mercury displaced from 

the space ABC in Fig. 61. The former case is often called 
capillary attraction and the latter capillary repulsion. 

152. Capillary Tubes, i. e., tubes of fine bore <Latin capillus, 
hair), are shown in Fig. 62. A wide tube does not affect the 



72 



LIQUIDS 



MR 



wm^^om 



Fig. 62. — Cross-section of 
tubes in water at 20° C. 
Actual size. 



general level of the water within it, the surface tension only- 
sufficing to raise the water in a curve around the walls. 
In A the curves due to surface ten- 
sion meet, and the pull of the film 
is- sufficient to raise the water above 
the general level. 1 In B and C the 
water rises higher, and in general 
the finer the bore of the tube the 
higher the water will rise. Capil- 
larity is partly responsible for the 
flow of liquids in the cells of plants. 
It raises the kerosene in the lamp- 
wick and gives to towels and 
blotting paper their usefulness. 

(A very interesting discussion of the subject of surface 
tension will be found in C. V. Boys' little book, Soap 
Bubbles.) 

153. Osmosis. The passage of liquids or gases through 
porous membranes or other partitions is called osmosis. 
The root-hairs of plants absorb liquids from the soil through 
their cell wails. This is one of a multitude of examples 
of osmosis presented in the life processes of animals and 
plants. 

154. Pressure is a term often used in connection with 
liquids, and it calls for accurate definition. When force is 
exerted upon a body, the area over which the force is dis- 
tributed is a matter of importance. Thus, a broad- wheeled 
wagon is not likely to make ruts in a road because its weight 
is distributed over a large area. We say that it exerts 
less pressure on the road than one of the same weight with 
narrow wheels. Pressure is estimated in units of force per 
unit area, as grams per square cm., lbs per sq. inch, etc. It 

U '4-4. D f 0rCe 

may be written r = . 

J area 



1 The curved surface which the liquid exhibits in a tube is called a 
meniscus. 



TRANSMISSION OF EXTERNAL PRESSURE BY LIQUIDS 73 

155. Elasticity of Liquids. About 1650 an experiment 
Was tried under the auspices of the Accademia del Cimento 1 
in Florence to determine whether or not water is com- 
pressible. A hollow sphere of silver was filled with water 
and sealed. It was then subjected to great pressure. The 
sphere was not dented, although the pressure was so great 
as to cause a little of the water to ooze through the 
metal. The academicians concluded that water is incom- 
pressible. Their apparatus did not admit of measurement 
accurate enough to detect the small amount of compression 
which occurred. 

156. Water does yield to a force tending to compress 
it. Suppose a cylinder whose cross-section is 1 square cm. 
filled with water at 0°C. and fitted with a piston, which is 
pushed in with a force of 1 kg. The volume of the water 
would be diminished about one-twenty-thousandth part. 
To reduce the volume 1 per cent, would require a pressure 
of 200 kilograms per square centimeter, or about lj tons per 
square inch. As soon as the pressure is removed the water 
returns to its former volume. Water is highly elastic, and 
so are liquids in general. In all of our discussion about 
pressure of liquids they are treated as if they were n ^ 
incompressible, since they yield so little to any 
ordinary forces. 

157. Transmission of External Pressure by Liquids. 
The diagram represents a vertical section of a vessel 
1 cm. square filled to a depth of 5 cm. with water. 
A piston, whose area is of course 1 square cm., is 
fitted water tight to the vessel, and a force of 1 
kilogram applied. Not only will the force against 
the bottom be now 1 kilogram greater than before, 

but every square centimeter which the water touches is pressed 
upon by a force 1 kilogram greater than before. It seems 

1 After the death of Galileo, Torricelli and a few other of Galileo's 
disciples founded in Florence the Accademia del Cimento (Academy 
of Experiment). Much important work in experimental science was 
done bv this society. 



74 



LIQUIDS 




at first glance surprising that a force should thus balance 
another so many times greater than itself. It is not 
more surprising than that a small force applied to the 
long arm of a lever will balance a large force applied to 
the short arm. In the case of the levers the moments 
are equal. In the case of the water the pressures are 
equal. 

158. A vessel filled with shot, subjected to pressure from 
above, experiences pressure on the sides, transmitted by 
the shot in the manner discussed in paragraph 139. In 
that case, however, friction of the grains of shot prevents 
the sidewise pressure from equalling that impressed upon the 
shot at the top. The internal friction of liquids at rest, 
for the reason explained in paragraph 
141, seems to be zero, and it is true in 
general that liquids at rest transmit 
pressure equally in all directions. 

159. The Hydrostatic Press makes use 
of the fact just stated. The principle of 
its construction is shown in the diagram. 
The vessel has two cylinders fitted with pistons P and p, and 
is filled with water. Let the piston p have an area of 1 
square inch and P 25 square 
inches. A force of 10 pounds 
at p will balance a force of 250 
pounds at P. The mechanical 
advantage may be further in- 
creased by means of a lever 
attached to p. Fig. 65 shows 
a small hydrostatic press. 
The lever operates a small 
piston, which forces water 
drawn from a reservoir in the 
base into the large cylinder. 
Because of the small internal 
friction of liquids the efficiency of the hydrostatic press is 
high, sometimes as much as nine-tenths. It is used for lift- 



Fig. 64. — Principle of 
hydrostatic press. 




Fig. 65. — Hydrostatic press. 



T 



TOTAL FORCE AGAINST THE BOTTOM OF A VESSEL 75 

ing heavy weights, for baling cotton, and for many other 
purposes where a great force is needed. 

160. Pressure of Liquids due to Gravity. Liquids exert 
pressure on the containing vessel and on objects immersed 
in them, because of their weight. This 
pressure is exerted in all directions, as 
may be shown by filling with water a 
vessel having holes in the bottom and 
sides, and thrusting into it a smaller, 
empty vessel having a hole in the 
bottom. Water will flow down as at A 
horizontally as at B and upward as at 
C, because of the pressure of the water 

behind. The pressure due to the weight of the liquid is, 
of course, exerted upon the liquid itself as well as upon 
immersed objects and the containing vessel. 

161. Imagine a particle in a vessel of water at rest. It 
is pressed upon in every direction by the surrounding 
water, and since it is at rest, the forces in any two opposite 
directions must be equal. Otherwise the particle would 
move in the direction of the greater force, and the liquid 
would not be at rest. At any point in a liquid at rest, the 
pressure in all directions is equal. This pressure is pro- 
portional to the depth below the free surface and to the density 
of the liquid. At a point 1 meter below the surface of pure 
water at 4° C. the pressure is 100 grams per square cm., 
2 meters down it is 200 grams, etc. Sea-water is 2 \ per 
cent, denser than fresh, so that the pressure at a given depth 
is 2.5 per cent, greater. The pressure on sea-water at a depth 
of 1 mile is not quite enough to compress it 1 per cent. 

162. Total Force against the Bottom of a Vessel. If the 
vessel has vertical sides and the bottom is horizontal as 
in A the total force against the bottom is simply the weight 
of the water. Suppose the bottom to be 10 cm. square and 
the water 15 cm. deep. The pressure on the bottom will 
be 15 grams per square cm., and the total force will be as 
many times 15 grams as there are square centimeters in the 



76 



LIQUIDS 




Fig. 67 



bottom, or 15 X 100 = 1500 grams. The volume of the 
water is 15 X 10 X 10 = 1500 cubic centimeters, so that it 
weighs 1500 grams, which is the same as the force against 
the bottom. In the ves- 
sel B, since the depth of 
the water is the same, the 
pressure at the bottom 
will be the same, 15 gr. 
per sq. cm., and since the 
area of the bottom is the 
same, the total force as before will be 1500 grams. The 
same will be true for the vessel C. 

163. These results may be perhaps more easily stated 
than appreciated. In the case of B it may be noted that the 
force due to the weight of the water in the spaces D is exerted 
on the sloping sides of the vessel. In the case of C, the up- 
ward force due to the pressure of the water against the 
surface EF is met (Newton's third law) by an equal and 
opposite force, the resistance of the wall of the vessel. This 
force is added to the weight of the water below EF, and 
thus the total force against the 
bottom is the same as in the case 
of the vessel A. 

164. Pascal's Vases. Pascal 1 de- 
monstrated that the pressure on 
the bottom of a vessel is inde- 
pendent of the shape or size of the 
vessel. He used apparatus similar 
to that shown in Fig. 68. The cord 
attached to the arm of the balance 
holds in place a plate which fits 
watertight against the end of a tube 
within the lower vessel and forms 
the bottom of a vessel the upper part of which is funnel- 
shaped. .Weights are put on the other arm of the balance so 
that if the funnel-shaped vessel be gradually filled with water, 

1 Blaise Pascal, French philosopher, 1623-1662. 




Fig. 68. — Pascal's vases. 



PROBLEMS AXD EXERCISES 77 

the bottom will be pushed off just before the vessel is entirely 
filled. The index shown at the side is set so that its point 
indicates haw high the water rose before the bottom was 
pushed off. If the funnel-shaped vessel be now unscrewed 
and the other two vessels substituted in turn, it will be found 
that the same depth of water in each case suffices to push off 
the bottom, although the quantity of water is very different 
in the three cases. 

165. Pressure on the Sides of a Vessel. The simplest case 
is that of a rectangular vessel whose sides are vertical. 
Suppose the vessel in the diagram to be 4 cm. square and filled 
with water to a depth of 8 cm. The pressure against the side 
AB at the bottom is equal to that against the bottom, 
8 grams per sq. cm. Any square cm. of the bottom is 
pressed on with a force of 8 grams, but there is no square 
centimeter of the side which sustains a force 
so great as 8 grams. At C } one cm. from the 
bottom, the pressure is 7 grams per square 
cm. and the actual force on a square centi- 
meter extending from the bottom to C is 1\ 
grams. The horizontal pressure at the sur- 
face is zero, and the average value of the 
pressure between A and B is the average 
between 8 and 0, since the pressure increases " F 6q 
uniformly from A to B. The average is 4 
grams per sq. cm., therefore the whole force on AB is the 
product of 4 grams by the number of square centimeters in 
its area = 128 grams. The entire force on the interior of 
the vessel is, of course, four times this amount, plus the 
force on the bottom = 640 grams. In the case of vessels 
of irregular shape, the problem of the sum of the forces 
exerted by water contained in them may be very complex. 

PROBLEMS AND EXERCISES. 

1. From the top of a cliff 96 feet high, how far at sea may 
a row-boat be seen? 



78 LIQUIDS 

2. An observer on shore just sees the pennant at the top 
of a mast, the rest of the ship being below the horizon. If 
the distance is 13 miles and the observer's eye at the surface 
of the water, how high above the water is the pennant ? 

3. The eye of an observer in a light-house is 150 feet above 
the water. How many miles away can he see an object 
on the surface of the ocean? How many miles farther 
away may a ship be, and its pennant 96 feet above the water 
be visible to the observer in the light-house? 

4. It has been proposed to run a small water-wheel with 
water raised by capillary tubes, the water returning to the 
vessel from which it was drawn, to be again raised by the 
tubes and run over the wheel. Will such a plan work? 

5. Why is writing paper " glazed," while blotting paper is 
not? 

6. Why is a soap bubble spherical? 

7. Why is not water as suitable as alcohol for use in levels? 

8. A large bottle of rather thin glass was filled with vinegar 
to the top. A cork being forced in, the bottom of the bottle 
burst out. Explain. 

9. In a hydrostatic press the small piston is 1 inch in 
diameter and the large one 6 inches. The small piston is 
operated by a lever whose mechanical advantage is 10. 
Allowing yq- for friction, how heavy a load may be lifted by 
a force of 100 lbs. on the lever? 

10. The internal dimensions of a rectangular vessel are 
10, 20, and 40 cm. respectively. When the vessel is filled 
with water and its largest face is horizontal, find the sum of 
the forces on the bottom and sides of the vessel due to the 
weight of the water. Also find the sum of the forces when the 
vessel stands on its edge, and on its end. 

166. Buoyancy. Suppose a cube whose edge is 1 cm. 
immersed in water to a depth of 1 cm. (Fig. 70). The 
downward force on the upper surface is 1 gram, and the 
upward force on the lower surface 2 grams. The resultant 
of these two opposed parallel forces is 1 gram directed 



FLOTATION BY SURFACE TENSION 



79 




Fig. 70 



upward. This upward force exerted upon the block, called 
buoyancy, is equal to the weight of the water displaced. Every- 
body immersed in water, whether wholly or 
partly, is thus buoyed up by the water. If 
the body weighs just as much as the dis- 
placed water, it remains in position; if it 
weighs more it sinks, while if it weighs less 
it is pushed up. 

167. Floating Bodies. A block of pine 
wood pushed down in water and released, 

rises to the surface, and will presently settle in such a posi- 
tion that the weight of the displaced water is just equal to 
the weight of the body. It is evident that this must be so, 
for the buoyancy of the water is equal to the weight of 
water displaced, and when the block 
floats, the force of gravity downward is 
just balanced by the buoyant force. 
It may be experimentally proved that 
a floating body displaces its own weight 
of water. Water is poured into the 
vessel C, Fig. 71, until it flows away at 
the outlet 0. Then a weighed vessel 
V is so placed as to catch any further overflow, and a 
weighed piece of wood F is placed in the water. When the 
water ceases to flow into V, it will be found that the water 
in V weighs nearly as much as F. Owing to surface tension 

effects, the water does not always run 

out so as to make the level after intro- fe^T^ilwJI 
ducing the floating body just the same 
as before. 

168. Flotation by Surface Tension. If 
a fine needle be drawn through an oily 
rag so as to coat it with a thin film 
of oil, and then very carefully laid on a still vessel of 
water by means of a bent wire W, it will float. The 
water does not adhere to the oiled needle, so that the 
surface film is not interrupted. The water displaced by 



Mm 



Fig. 71 



Fig. 72. — Cross-section 
of needle on water. 



80 



LIQUIDS 



the depression of the surface film is equal in weight to the 
needle. 

169. Water-spiders float in the same manner. The water 
does not wet their feet, and each foot rests in a tiny depres- 
sion. The sum of these several quantities of displaced 
water is equal in weight to the spider. A cat could walk on 
water if a film of rubber a millimeter thick were stretched 
over the water. 



EQUILIBRIUM OF FLOATING BODIES. 



4& 



<V 



Fig. 73 



170. Centre of Buoyancy. The diagram represents an ob- 
ject floating on water, G being its centre of gravity. The 
buoyant force of the water acts through the point B, the 
centre of gravity of the dis- 
placed water, called the centre 
of buoyancy. The force of 
gravity and the buoyant ~" 
force are, in general, a couple 
(paragraph 53) since they 
are equal and parallel and 
act upon different points. 

171. Stable Flotation. If, 

when a floating body is disturbed, the conditions are so 
changed as to give the couple a moment tending to restore 
the body to its previous position, the body is stable, its 
stability depending on the magnitude of the restoring 
moment due to a given displacement. If the floating body 
of Fig. 73 a be tilted into the position of Fig. 73 b, the 
centre of buoyancy shifts toward the right, and the couple 
has a moment tending to bring the body to its previous 
position. 

172. Unstable Flotation. Fig. 74 a represents a board float- 
ing on edge in equilibrium ; b shows the same board disturbed. 
The tilting has called into play a moment which tends to 
make the board go on in the direction in which it has been 






BOATS AND CANOES 



81 



started. 1 The equilibrium was therefore unstable. If the 
board be loaded on one edge with lead, it will float on 
edge. A floating object is always stable when its centre 
of gravity is below its centre of buoyancy (Fig. 75). 





Fig. 75 



173. Neutral Flotation. A homogeneous floating sphere 
or cylinder is in neutral equilibrium because it may rotate 
without changing the position of the centre of buoyancy, 
and therefore without calling 
into play any restoring or up- 
setting moment. 

174. Boats and Canoes. The 
form of cross-section shown in 
Fig. 77, common in boats, is 
very stable, since a disturb- 
ance causes more water to be 

displaced on the side toward which the boat tilts, and less on 
the other, thus rapidly shifting the centre of buoyancy. If 
the cross-section is an arc of a circle, a tilt causes no shift of 
the centre of buoyancy, and the only way such a boat can be 
kept stable is by keeping the centre of gravity below the 
centre of buoyancy. Canoes are apt to be more nearly 
round-bottomed than other boats, and it is dangerous to 




Fig. 76 



Fig. 77 



1 It is a curious fact that if the density of the board is .5, its centre 
of gravity neither rises nor falls as it swings into its position of stability, 
but if its density is less than .5 the centre of gravity falls, and if 
greater it rises. There are many problems of great interest connected 
with equilibrium of floating bodies. 
6 



82 LIQUIDS 

stand up in them unless one is very skilful, because raising 
the centre of gravity of the boat and its load may render 
it unstable and cause it to turn over. 



DENSITY OF SOLIDS AND LIQUIDS. SPECIFIC GRAVITY. 

175. Archimedes and the Crown. Hiero, King of Syracuse, 
gave to a goldsmith a weighed quantity of gold to be made 
into a crown. When the crown was brought to the King, he 
found the weight correct, but suspected the goldsmith of 
having taken a part of the gold and substituted a cheaper 
metal. He commissioned Archimedes to discover without 
injuring the crown whether there had been any fraud. 
The problem was a new one, and Archimedes was still pon- 
dering it when he went to the public baths. Here, it is said, 
the attendant had filled the tub quite full, and when Archi- 
medes got in the water overflowed. He saw that a body as 
heavy as himself but occupying less space would have caused 
less water to overflow. This suggested a solution of the 
problem, and he was so overjoyed that he immediately 
rushed out into the street, shouting "I have found it! 
I have found it !" (Greek, Eureka.) He took a mass of gold 
equal in weight to the crown, and immersing it in a vessel 
full of water, weighed the water which overflowed. When 
the crown was immersed, a larger quantity of water over- 
flowed, showing that some less dense (or as we commonly 
say, lighter) metal had been mixed with the gold. 

176. Principle of Archimedes. The fact already stated 
on p. 79 that a body in water is buoyed up by a force equal 
to the weight of the water it displaces, is called the Principle 
of Archimedes. It applies to floating bodies and others 
partially immersed, as well as to those totally immersed. 
As has already been noted, the buoyant force in the case of 
floating bodies is equal to the weight of the body. A striking 
proof that the buoyant force exerted on a body entirely 
immersed is equal to the weight of an equal volume of water, 
is given by the apparatus shown in Fig. 78. 



DENSITY OF A STONE 



83 



A solid brass cylinder fits snugly into a brass vessel. The 
vessel is hung on one arm of a balance, the cylinder being 
suspended below it. Weights are now 
put in the other pan (not shown in the 
figure) to balance the cylinder and 
vessel. Then a jar of water is so placed 
that the brass cylinder hangs in it, being 
just immersed when the beam of the 
balance is level. The buoyancy of the 
water pushes the cylinder up. Water 
is now poured into the vessel, and the 
cylinder gradually sinks in the water. 
When the vessel is just filled the beam 
is level and the cylinder immersed. The 
buoyant force of the water in the jar 
pushes the cylinder up with a force just equal to the weight of 
the water in the vessel, which is equal in volume to the cylin- 
der. The weight of a completely immersed object is diminished 
by an amount equal to the weight of an equal volume of water. 

177. Density of a Stone. The density of a substance has 
already been defined (paragraph 13). It is the number of 

M 

units of mass in one unit of volume. D = — . where 




Fig. 78.— Cylinder 
and bucket experi- 
ment. 



V 



M is the number of grams in a definite portion of the sub- 
stance, and V the number of cubic centimeters which this 
portion occupies. 

In order to determine the density of a body, it is in general 
necessary, then, to find its mass and its volume. The 
mass is found by weighing in air, and, if very accurate re- 
sults are required, correcting this result for the buoyancy 
of the air. If the body is rectangular or of some other geo- 
metric shape, its dimensions may be measured and its volume 
computed. Thus a rectangular piece of steel 1x2x5 cm. 
in size has a volume of 10 cc, and if its mass is 75 grams 
its density is 7.5. 

178. If, however, the object whose density is sought i^ 
irregular in shape, its volume cannot be found directly. 



84 LIQUIDS 

The principle of Archimedes affords a convenient indirect 
means of finding such a volume. The difference in the 
weights in air and in water gives the weight of the displaced 
water, and if this be in grams we have at once the volume 
of the body. Of course the body must be entirely immersed 
in water in making the second weighing, and if the most 
accurate results are required the water must be pure and 
free from air and at 4° Centigrade. The weighing in water 
is commonly done by suspending the object by means of a 
fine thread to a hook fastened to the pan of the balance. 
Suppose a piece of stone to weigh 50 grams in air and 30 
in water. The displaced water is 20 grams and therefore 
20 cc. The volume of the stone is therefore 20 cc, and 
its density 50 -s- 20 = 2.5. That is to say, 1 cubic centi- 
meter of the stone contains 2.5 grams. This method is 
used for any solid that sinks in water and is not soluble 
in it. 

179. The Density of a Solid which does not Sink in Water 
may also be found by the principle of Archimedes. In this 
case, however, the weight of the body in water is negative, 
because when immersed it pulls up instead of down, and of 
course it displaces an amount of water whose weight is 
greater than its own. This negative weight or upward pull 
may be found by seeing how much the object lightens a 
sinker previously weighed in water. Suppose a piece of 
pine wood weighs 20 grams. A suitable sinker will be a 
strip of lead about 3 mm. thick, 10 cm. long, and 1.3 cm. 
wide, weighing about 40 grams in air and 36 in water. When 
the wood has been weighed in air and the lead in water, 
wrap the lead around the wood and weigh both in water. 
The two may weigh 6 grams in water. The upward pull of 
the wood is therefore 30 grams, since the lead alone weighs 
36 grams in water, and the wood and lead only 6. The water 
supports the whole weight of the wood and 30 grams besides, 
by its buoyant effort exerted on the wood. The wood acts 
as a life-preserver for the sinker, and if the lead were a few 
grams lighter the wood would float it. Now the displaced 



DENSITY OF LIQUIDS BY BALANCING COLUMNS 85 



water is 20 + 30 = 50 grams = 50 cc, and the density of 

the pine wood 20 -r- 50 = .4. 

180. It is well also to work out our problem in the same 

manner as with the stone, and see that the two are precisely 

.. . _ . wt. in air 

parallel. In that case we had 



wt. in air - 
Here the weight in water is — 30. 



The density then is 



wt. in water 
So far from pull- 

20 
20 — ( — 30) ~ 



density. 

ing down, it pulls up 30. 

20 + 30 

181. Density of Liquids by Weighing. If a bottle be 
weighed, then filled with water up to a well-defined mark 
on the neck, and weighed again, the .difference gives the 
weight of the water, and this expressed in grams gives the 
volume of the bottle up to the mark in cc. Now if the 
bottle be filled to the same mark with another liquid and 
weighed, we have the weight of a known volume of the liquid 
and so find its density by division. A bottle weighs 60 grams. 
Filled with water to a certain point it weighs 160 grams. 
The volume up to the mark is therefore 100 cc. Filled 
to the same mark with alcohol it weighs 140 grams. The 
100 cc. of alcohol therefore weigh 80 grams, 
and the density of the alcohol is .8. 

182. Density of Liquids by Balancing Columns. 
Two liquids which do not mix may be compared 
by the method shown in the diagram, which 
represents a glass U-tube mounted vertically 
with a meter-stick between its arms, filled from 
B to A with water and from A to C with a light 
oil. The water in the two arms below AE bal- 
ances itself, so to speak, and the water in the 
column BE balances the oil in the column 
AC. The two columns balance because of 
equal pressures at A. The weight of liquid in BE is not 
necessarily equal to that in AC, but they will be equal if the 
tube has a uniform bore. The pressure exerted by a liquid at 



E 



wC 



Fig. 79 



86 



LIQUIDS 



AC and of BE. We have 



density of water 
density of water is 1, therefore the density of the oil= 



But the 



£ 



a given point depends on the depth below the free surface 
and on the density of the liquid. If two liquids exert equal 
pressures at a given point, the one whose density is less 
must make up for that by proportionately greater depth. 
If the liquid in AC is but half as dense as water, the column 
AC must be twice as high as BE. To find the density of 
an oil by this method, measure the vertical height of 

density of oil BE 
" = AC 

BE, 
AC 

183. If the liquids are such as would mix, the apparatus 
shown in Fig. 80 is used. The two tubes, dipping into the 
two liquids in A and B, are connected at the top 
to the rubber tube R. Some air is withdrawn 
from R and the stopcock S closed. The liquids 
are now supported at heights BE and AC which 
are as before inversely proportional to their den- j$ 
sities, since they are supported by equal press- 
ures, the difference between the pressure in the 
tube R and that of the atmosphere. 

184. Hydrometers are used in practice for 
finding the density of liquids. A simple hydrom- 
eter is shown in the diagrams, consisting of a 
prism or cylinder of wood weighted at the lower 
end so as to float upright in a vessel of water. 

The wood should be coated with paraffin to keep the water from 

soaking into it. Floating the hydrometer in water as in A, mark 

the point c at which the surface meets it. 

Then float it in another liquid, denser than 

water. It floats higher than before. Mark 

the point d at which it floats. Now the 

displaced quantities of the two liquids 

have equal weights, each equal to the 

weight of the hydrometer. The displaced 

volumes are proportional to the lengths ac /; 

and ad, and are inversely proportional to Fig. 81 



Fig. 80 



— 


1* 

a 




4 


1* 

6 
(t 



SPECIFIC GRAVITY 87 

the densities, since a denser liquid would require less volume to 

TTT . density of liquid B ac 

contain a gi ven weight. We have — -= rr ^ = — y 

° density ot water ad 

The densities of any two substances are inversely proportional 

to the volumes of equal weights. 

185. Specific Gravity. This term is often used instead of 
density. In the case of solids and liquids specific gravity 
and density are numerically equal in the C. G. S. system, 
although their definitions are different. The adjective 
specific as used in physics implies a comparison with some 
standard. In this case the standard is water, and the specific 
gravity of a substance may be denned as the ratio of the 
weights of equal volumes of the substance and of water. 

It is clear that most of the methods described for finding 
density apply equally well to the determination of specific 
gravity. A stone is weighed in air and in water. The 
difference of these weights is the weight of an equal volume 
of water. This divided into the weight of the stone gives 
its specific gravity. In finding density we considered the 
number of cc. of displaced water. Here we use the number 
of grams, which is the same. The weight may of course 
be taken in ounces or grains as well as in grams, but in that 
case we could only find the volume by calculation. Instead 
of finding the volume, if the density is required where a body 
has been weighed in grains, we simply compute the specific 
gravity and then the density is known, since they are numeri- 
cally equal. 

186. In the case of liquids the weighing method evidently 
gives specific gravity, since we are comparing weights of 
equal volumes. For the other methods described the prob- 
lem is not quite so simple, but since the hydrometer method 
is the one most frequently used in practice, let us examine 
that. Here only one weight is involved, that of the hydrom- 
eter, which in the case of the one already described, is 
constant. It sinks to different depths in different liquids, 
and by using a number of liquids whose specific gravity 
has been determined by weighing, points may be marked 



88 LIQUIDS 

on the stem of the hydrometer forming a scale from which 
the specific gravity of an unknown liquid may be immediately 
read. 

187. It is clear that equal differences in specific gravity 
will not be represented on the scale by equal spaces. A 
common form of hydrometer is shown in the dia- 
gram. It is made of glass, with a cylindrical stem 
containing the scale, and two bulbs. The lower 
small bulb is filled with mercury or shot and the 
other with air. The scale is often an arbitrary one of 
equal parts, that of Baume being the most common 
(Fig. 82). Such hydrometers are commonly marked 
either "for heavy liquids" (floating in water nearly © 
immersed) or "for light liquids" (floating in water Fig. 82 
with the whole scale projecting). 

Sometimes both Baume's scale and a scale of specific 
gravities are given on the same instrument. These hydrom- 
eters are commonly used for testing acids, ammonia, etc., 
but many other forms are made. The sensitiveness of a 
Baume hydrometer is increased by making the stem slender, 
but its range is at the same time decreased. A table for 
converting Baume degrees into specific gravities is appended. 





Heavy liquids. 


Light liquids. 


Baume 


Specific gravity. 


Baume. 


Specific gravity 





1.00 


10 


1.000 


10 


1.07 


15 


.967 


20 


1.15 


20 


.936 


30 


1.25 


30 


.880 


40 


1.36 


40 


.830 


50 


1.49 


50 


.785 



PROBLEMS IN DENSITY, ETC. 



1. A glass graduate contains 200 cubic centimeters of 
water. Two lead kilogram weights are put into it and the 
water rises to 382 cc. Compute the density of lead. 



PROBLEMS IN DENSITY, ETC. 89 

2. In the same graduate a piece of pine wood weighing 
50 grams raises the water from 200 cc. to 325 cc. Find the 
density. 

3. Determine the density of the following solids: 

Weight in air. Weight in water. 
Grams. Grams. 

Iron 47 41 

Sandstone 54 34 

Gold coin 33.412 31.478 

Lead 34.7 31.6 

4. Find the density of the following solids: 

Weight of 
Weight of body and sinker 
Weight in air. sinker in water. in water. 
Grams. Grams. Grams. 

White oak wood .... 24 40 32 

Pine wood .15 40 25 

Cork 10 40 9 

Bees' wax 18 40 38 

5. Under standard conditions (paragraph 461) a liter of 
air weighs 1.29 grams, of hydrogen .09 gram, and of carbon 
dioxide 1.98 grams. Find the density of each. 

6. A piece of rock salt weighs 56 grams in air and 36 
grams in kerosene. The density of kerosene is .793. What 
is the density of rock salt ? 

7. A cylindrical hydrometer floats 10 cm. deep in sulphuric 
acid and 20 cm. in ammonia water. The density of the 
ammonia is .89 ; find that of the sulphuric acid. How deep 
would this hydrometer float in water? 

8. A cylindrical hydrometer floats 20 cm. deep in alcohol 
and 16.4 cm. in water. Find the density of the alcohol. 

9. In a U-shaped tube arranged as in Fig. 79, containing 
kerosene and water, the following readings are taken on the 
meter-stick: junction of oil and water 5 cm.; top of water 
column 65 cm.; top of kerosene 80.7 cm. Find the density 
of the kerosene. 



90 LIQUIDS 

10. A bottle weighs 67 grams. Filled with water it weighs 
317 grams. What is the capacity of the bottle? Full of 
alcohol it weighs 267 grams. What is the density of the 
alcohol ? 

LIQUIDS IN MOTION. 

188. Liquids possess inertia and are acted on by forces, 
and in a general way obey the same laws as solids, but the 
fact that the molecules are free to move with respect to each 
other complicates the problems of moving liquids, so that 
their mathematical treatment is quite beyond the limits 
of this book. 

189. Waves. The friction of the wind against water 
surfaces causes the familiar motion which we call waves. 
These will be discussed in a later chapter in connection with 
other kinds of waves. 

190. Flow of Streams. A liquid flowing down a straight 
smooth trough would obey the same laws as a body rolling 
down an inclined plane, and the velocity of its molecules 
when it reaches the bottom would be the same as if it had 
fallen freely through the same vertical height, except for 
the modifying influence of friction. The layer of liquid 
next to the trough adheres to it, and is retarded, while the 
next layer adheres to the first, and so on. If the stream is 
very shallow, a millimeter or less, it soon reaches a limiting 
speed, as does a very small body falling in air. In natural 
streams, whose courses are crooked and full of obstructions, 
most of the energy of the stream is used in overcoming 
friction against obstructions and in internal friction of the 
water due to " eddies," so that the speed of flow does not 
increase with distance from the source. 

191. Flow from Openings in a Vessel. Water does not flow 
in a smooth cylindrical stream from a round hole in a thin 
metal vessel. The water on the inside approaches the hole 
in various directions, and the result is a stream somewhat 
like that shown in Fig. 83, smaller than the hole at a little 



FLOW FROM PIPES 



91 



distance from the vessel. If the opening be shaped as in 
Fig. 84 the water will issue in a smooth stream, and more 
water will flow out with a given pressure and size of opening 
than in the other case. If, however, a long pipe be attached 
to the opening, friction inside of the pipe diminishes the out- 
flow. The velocity of outflow from an opening in the side 





Fig. 83 



Fig. 84 



Fig. 85 



of a vessel, disregarding friction, is the same that a body- 
would acquire in falling freely through the vertical height 
from the level of the water surface to that of the opening. 
If s is this height, and v the velocity, v = \/2gs. This velocity, 
if the jet were directed vertically upward, would suffice to 
carry it up to the level of the water in the vessel, if it were 
not for friction and the resistance of the air (Fig. 85). 

192. Flow from Pipes. In Fig. 86, R represents a reser- 
voir full of water with a horizontal pipe AB. At various 
points along the 
pipe, glass tubes 
are connected to 
serve as pressure 
gauges. When the 
end B of the pipe is 
closed, the water 
in the tubes rises 
to the level CD. 

When B is open the tops of the columns in the tubes lie 
along the line CB. If the pipe is large and the opening at B 



— <7 


" z < 


— ~ 


-— - 










E 


E 






^^ 


-^ 


"v^ 






A 












^ 


B 



Fig. 86 



92 



LIQUIDS 



small we may get a pressure line somewhat like CE. This 
experiment suggests the reason for having large water 
"mains" in the street. It also throws some light on the 
difficulty we sometimes have in drawing water on the second 
floor of a dwelling when a faucet is open down stairs. 



WATER MACHINES. 

193. Overshot Wheel. This form of water-wheel utilizes any 
kinetic energy which the water may have, and also a large 
part of its potential energy. A 
part of the latter is lost because 
some of the water is spilled out of 
the "buckets" before it reaches 
the level of the water in the tail 
race. This form of wheel was for- 
merly much used for driving mills, 
but has been largely superseded 
by the turbine. 

194. Breast Wheel. This form 
is not quite so efficient as the overshot, partly because of 
leakage between the wheel and the curved "breast." It is 
sometimes used where there is a large quantity of water and 
not much fall. It also is being superseded by the turbine. 




Fig. 87. — Overshot wheel. 





Fig. 88. — Breast wheel. 



Fig. 89. — Undershot wheel. 



Undershot Wheel. This form is employed where there is 
much water and a swift current and the stream cannot be con- 
trolled so as to secure any fall. It uses kinetic energy only. 



TURBINE WHEEL 



93 




Fig. 90.— Barker's mill. 



195. Turbine Wheel. The principle of the turbine wheel 
is well illustrated by the scientific toy known as Barker's 
Mill, shown in the drawing. It con- 
sists of a vertical tube open at the 
top and having two or more branches 
at right angles to itself near the bottom. 
These branches have horizontally di- 
rected openings in one side near the 
end. The vertical tube with its 
branches has a vertical axis, and when 
water is poured in at the top the 
system revolves in a direction oppo- 
site to that of the escaping jets. In 
the detail diagram, Fig. 91, one of the 
openings is shown. The pressure due to the column of water 
in the vertical tube is exerted equally upon the wall of the 
tube at A and upon the escaping water at B. 
It is a case where Newton's third law applies, 
" action is equal to reaction." The water is 
pushed one way and the tube the other. 

196. The turbine wheel is made in many 
forms, most of which use the reaction of the 

escaping water, as Barker's mill does. Some use the kinetic 
energy of the moving water, and some use both. One of 
the many forms is shown in the dia- 
gram. Water descending the pipe 
P enters the chamber B and is 
directed by guide blades G against 
the vanes of the wheel W. It then 
passes through the wheel, and in 
escaping from it strikes at right 
angles the stationary blades T, and 
after passing through these flows 
away in the tail race. 

197. The turbine is superseding 
both overshot and breast wheels for jr IG 92.— Diagram of tur- 
most uses. There are several reasons bine water wheel. 



- -*J9 

ir 

Fig. 91 




94 



LIQUIDS 



for this. It is more efficient, often utilizing 80 per cent, of the 
energy applied. It can be operated at high speeds, so as to 
be available for driving dynamos and other high speed machin- 
ery without gearing or belts for " speeding up." It occupies 
little space in proportion to the power developed. It 
costs rather less than the older types. It usually runs 
immersed in water, so that it is not liable to freeze up in 
winter. It can be used with a very wide range of falls, from 
one foot to hundreds of feet. Many turbines are being in- 
stalled to drive dynamos to produce 
electric current for light and power. 
Those at Niagara Falls are the most 
notable examples. 

198. Impulse Wheel. Another form 
of wheel which is coming into use 
where great fall is available and the 
water-supply relatively small is shown 
in the diagram. The water issues 
from the small horizontal jet with 
great velocity, striking the curved 
blades, whose shape is such as to 
catch the water, so to speak. This wheel utilizes kinetic energy 
only, and is fairly efficient. When great fall is utilized, 
whether with this wheel or the turbine, a small quantity 
of sand in the water destroys the wheel very rapidly, wearing 
away the metal because of its high velocity. 

199. Hydraulic Ram. A small water-wheel driving a force- 
pump (see paragraph 251) is often used to supply water 
for country houses, but where the amount needed is not 
more than two or three hundred gallons a day, a much less 
expensive device called the hydraulic ram is employed. In 
the diagram, S is the spring or other source of the water 
which flows down the drive pipe D and out at the valve R, 
shown in detail at the left. As the water continues to flow, 
its velocity increases, and it pushes the driving valve R 
harder, until it suddenly shuts with a shock. The moving 
stream of water in the drive pipe strikes a blow like a hammer 




Fig. 93. — Diagram of im- 
pulse water wheel. 



HYDRAULIC RAM 



95 



against the inside of the pipe. This blow lifts the valve 
V, forcing a little of the water through it into the air-chamber 




Fig. 94. — Diagram of hydraulic ram. 

A. The elasticity of the water causes it to rebound, allowing 
the valve R to drop and V to close. Then the water in D 
begins to flow again and the process is repeated. 

200. The air in A is compressed and forces the water up 
the pipe P. The air yields each time the driving valve 
strikes, and keeps up its pressure on the water between 
strokes, so that a steady flow through P is kept up. The 
office of the air-chamber is like that of the fly-wheel, to 
transform intermittent into continuous work. 

201. Water may be raised by the hydraulic ram to a height 
many times greater than that from which it came. If a 
fall of ten feet forces the water 100 feet high, a perfectly 
efficient machine would send up only one-tenth of the total 
flow. In practice the proportion would be much less. 

202. The air in the air-chamber gradually dissolves in the 
water, particularly in cold weather (paragraph 481), and thus 
the air-chamber tends to fill with water. If it becomes 
full, the quantity of water sent through the pipe P is much 
reduced, most of the energy of the water in D being expended 
in overcoming the inertia of the water in P, which must be 
done for every stroke. In order to prevent the air-chamber 
from filling, a tiny hole is often made in the drive pipe just 
outside the air-chamber. When the water recoils a bubble 
of air is sucked in, and a part of this air finds its way into 
the air-chamber and so keeps up the supply. 



96 



LIQUIDS 



203. It might appear that the hydraulic ram overcomes 
a greater pressure, that of the high column of water in P, 
by means of a less pressure, that of the water in D. It is 
not, however, a matter of pressure. With a hammer a man 
drives a nail which he could not possibly push in. The kinetic 
energy of the hammer, J mv 2 , is applied to overcome the 
friction F of the nail through a space S, and so do work 
FS upon the nail. To push the nail in would require a force 
greater than F. But any hammer blow not so slight as to 
be all dissipated in heat will drive the nail some, and by 
making the velocity great, a small hammer will drive a nail 
against very great friction. So the \ mv 2 of the moving 
water in D does work on the water in P, overcoming its 
pressure for a small space. The work done is measured 
by the weight of water delivered multiplied by the height. 

204. The size of the pipe P is not important, except that it 
must be large enough to avoid undue friction, since it is only 
the force required to lift the valve V that has to be considered, 
and that depends only on the area of the valve and the height 
of the column. The pipe D, however, must have a consider- 
able size and length, in order that there may be a large 
m in the ^ mv. 2 It is slow work to drive a six-inch spike 



D should be straight, and smooth 
the 




with a tack hammer, 
inside, in order that 
water may flow as freely as 
possible, and must not be 
very long, because the in- 
ternal friction becomes too 
great. 

205. Hydraulic Lifts. Ele- 
vators are often operated 
by apparatus similar to the 
hydrostatic press. In the 
hydrostatic press the rate 

of motion is slow, and the total force is the principal matter 
considered, but in the elevator there must be a rapid flow of 
water in order to move the elevator at sufficiently high speed. 



S' 



Fig. 95. — Diagram of hydraulic lift. 



PROBLEMS AXD EXERCISES 97 

The simplest form of hydraulic elevator is illustrated in the 
diagram. The pipe A brings water from the city supply or 
from a special reservoir at the top of the building. The 
stopcock S admits water to the cylinder C, forcing up the 
piston P, and with it the elevator platform E. When S is 
closed and S' opened, the elevator descends by its own weight, 
and the water is forced out at S f . 



PROBLEMS AND EXERCISES. 

1. A cubic foot of water weighs (nearly) 62.5 pounds. 
47 cu. ft. per second are delivered on an overshot wheel 20 ft. 
in diameter. Considering only the potential energy of 
the water, and supposing the wheel to utilize 75 per cent, of 
it, how many horse-power does the wheel develop? 

2. What reason can you suggest for delivering the water 
under the turbine wheel, in Fig. 92? 

3. The great turbines at Niagara utilize about 150 feet 
fall. If the efficiency is 80 per cent., how many cubic feet 
per second are required to develop 5000 horse-power? 

4. In places where the rise and fall of the tide is great, 
the water of the high tide is caught in reservoirs and used 
to develop power while the tide is low. What kind of wheel 
would be best for such use? 

5. Small models of the hydraulic ram are made for use in 
the class-room. Is it well to use a rubber tube for a driving 
pipe? 



CHAPTEK IV. 

GASES. 

206. The difference between solids and fluids and between 
liquids and gases has already been stated (paragraph 137). 
Just as no sharp line can be drawn between solids and 
liquids, so there is none between liquids and gases, but the 
border land in this latter case lies among extraordinary 
conditions of temperature and pressure, and a discussion of 
it is beyond the scope of this book. 

207. Kinetic Theory of Gases. The force which causes the 
particles of a gas to repel one another is due to heat. They 
are in continual rapid motion and rebound from one another 
in much the same manner that elastic solids do. On account 
of the motion of their molecules gases have a tendency 
to expand, apparently without limit, so that a cubic centi- 
meter of air released in a perfectly empty space a cubic 
meter in extent would quickly fill the whole space. This 
tendency of air to expand is strikingly shown by placing 
in a glass vessel connected with an air pump (paragraph 241) 
a toy balloon or foot-ball " bladder" with but little air in it 
and the opening tied up, and then exhausting the air from 
the glass vessel. The small quantity of air in the rubber 
bag expands and fills and even distends the bag. 

208. Pressure due to Gases. In consequence of the motion 
of the molecules of gases, they are continually striking against 
the walls of the containing vessel, and thus exerting press- 
ure upon it, not only on the bottom and sides but on the 
top as well. This fact of pressure is shown in the disten- 
tion of the rubber in the experiment just described. The 
pressure on the bottom of a vessel filled with gas is of 
course greater than that on the top, on account of the weight 

(98) 



THE ATMOSPHERE 99 

of the gas, but in the case of small vessels this difference is 
so slight as to be negligible when we are considering the force 
per square centimeter or square inch. 

209. Diffusion of Gases. Not only do gases spread in empty 
space, but in space already occupied by other gases. Every 
gas spreads as uniformly throughout the space as if the others 
were not there, although not so rapidly. This slowness is 
due to the collisions of the molecules. If the space is empty 
the moving molecules pass into it without hindrance, but 
when it is already full of gas the molecules of the gas first 
considered must be many times sent backward and forward 
among those already present before they are evenly dis- 
tributed all over the vessel. In this respect gases behave 
much like such a pair of liquids as alcohol and water. Not all 
liquids, however, thus diffuse into each other, but all gases 
diffuse freely through one another. 

210. Compression of Gases. The experiment of paragraph 
207 shows that gases expand under diminished pressure. 
They also contract under increasing pressure. 

Let C be a cylinder in which a piston P works [j |[_ 

air tight. The piston may be pushed down to 

P' ', even if no air escapes, compressing the air 

beneath the piston into J its previous volume. 

The number of molecules striking the piston in 

one second would now be twice as great as Fig. 96 

before, and the pressure of the gas against it 

twice as great as before. Gases may be compressed very 

much, and will at once expand when the pressure is released. 

That is to say, gases are elastic. 

211. Air is the typical gas. It is believed that under 
ordinary conditions far less than one thousandth of the 
space occupied by the air is taken up by the molecules 
themselves, the rest being merely the space in which the 
molecules are darting about. Perhaps this explains in a 
way why gases are so compressible. 

212. The Atmosphere varies somewhat in its composition. 
We are apt to limit the term air to the oxygen, nitrogen, and 



100 GASES 

argon with its associated gases. Besides these there is always 
a nearly constant proportion of carbon dioxide and a very 
variable one of water vapor, besides traces of other things. 
We say that the air contains these things, just as water 
often contains in solution things which are really not a part 
of the water. Carbon dioxide is usually present in the 
proportion of about 3 parts in 10,000. It is of great impor- 
tance because it furnishes most of the food of plants. The 
proportion of water vapor varies very much, from a small 
fraction of 1 per cent, up to about 3 per cent. The pro- 
portions of oxygen and nitrogen are stated for air from 
which the water vapor and carbon dioxide have been re- 
moved. Oxygen, which is so necessary to the life of animals, 
makes up about 21 per cent., nitrogen more than 78 per 
cent., and argon with its companion gases less than 1 per 
cent. 

213. Height of the Atmosphere. A gas cannot have a 
free surface like a liquid, because the molecules fly apart. 
The density of the atmosphere diminishes as the distance 
above the earth's surface increases, because of the decreasing 
weight of air above it. Thus the atmosphere fades out 
gradually, and no limit can be assigned to it. Observations 
of meteors have shown that they begin to glow at heights 
sometimes approaching 100 miles. The glow is due to the 
resistance which the air offers to the swift-flying particles, 
so there must be air as high as 100 miles above us. 

214. Density of Air. Under ordinary conditions a liter 
of air weighs a little more than a gram, and a cubic foot 
a little more than an ounce. If a light metal vessel be 
accurately counterpoised on a balance, and then exhausted 
by means of an air pump and again weighed, it will be found 
lighter than before. If it be now just immersed in water 
and the water allowed to enter, the water wiped from the 
outside and the vessel again weighed, the number of grams 
of water which have entered will show very nearly how many 
cubic centimeters of air were withdrawn, and thus enable us 
to compute the density of the air. 



BALLOONS 101 

215. Specific Gravity of Gases is reckoned with reference 
to air. Values for several gases are here given: 

Specific Gravity and Density of Gases at 760 mm. Pressure 

AND 0° C. 1 

Specific gravity. Density. 

Air 1.000 .00129 

Oxygen 1.105 .00143 

Nitrogen 972 .00126 

Hydrogen 0696 .00009 

Carbon dioxide 1.529 .00197 

Coal gas (approx.) 400 .00050 

Chlorine 2.422 .00313 

216. Buoyancy of the Air. Objects surrounded by air 
are of course buoyed up by it with a force equal to the 
weight of the air displaced. This buoyant force is relatively 
so small that in the case of ordinary objects we do not think 
of it, and we correct weighings for the buoyancy of the air 
only where great accuracy is required. A mass of gas less 
dense than the surrounding air, enclosed in a thin enough 
envelope will rise. A soap-bubble filled with warm air 
from the lungs will rise in a cool room. Warm air rises 
through cooler air without being enclosed, as is shown in 
the " draft" up the chimney. Air expands when heated, 
becoming of course less dense, and the buoyant force of the 
surrounding air causes it to rise. 

217. Balloons. The first balloons were similar in principle 
to soap-bubbles, filled with heated air. Such " fire balloons," 
made of strong thin paper, are often sent up as a part of 
fire-works displays. The warm air gradually escapes through 
the paper, and a fresh supply is kept up by a sort of candle 
placed in the opening at the bottom. 

218.. Balloons intended to carry passengers are made of 
silk, varnished or rubber coated, and filled with illuminating 
gas or hydrogen. Hydrogen weighs about one-fifteenth as 

1 See paragraph 461. 



102 



GASES 




Fig. 97.— Balloon. 



much as air. A balloon displacing 6000 cubic feet would 
be filled by hydrogen weighing about 500 ounces at' 32° F., 
and displacing 7700 ounces of air. The difference, 7200 
ounces, or 450 pounds, would be the 
weight of gas-bag, car, passenger and 
equipment which such a balloon 
would carry at the freezing temper- 
ature. Balloons of the type shown 
in Fig. 97 have been much used in 
the past for scientific purposes and 
for the amusement of adventurous 
people and curious lookers on. The 
greatest height ever reached in one 
was about 7 miles. This was done 
by two English aeronauts in 1862, 
and again by a Frenchman in 1901. 
The earlier observers suffered in- 
tensely from the cold and from the 
rarity of the air, which at that height is only about J as 
dense as at the surface. The more recent ascent was made 
with less discomfort, the aeronaut inhaling compressed 
oxygen which was taken along. Balloons of this type can 
only travel as the wind carries them. 

219. Air-ships. Many successful flights have been made 
in recent years by balloons of another type. In these the 
gas-bag is long and pointed to enable it to pass through 
the air more easily, and the car carries a motor which drives 
a propeller. Such " air-ships" are also provided with one 
or several rudders, by which the direction of flight can be 
controlled. It seems not impossible that such dirigible 
balloons may come to have some practical value, especially 
in exploration, but it is likely that most of the business of 
mankind will long continue to be transacted on or below the 
surface of the earth. 

220. Pressure of the Atmosphere. The air contained in an 
ordinary vessel exerts but little pressure in consequence of 
its weight. At the bottom of a vessel of air 1 meter deep, 



DROPPING TUBE 



103 




Fig. 98 



the pressure is greater than at the top by about .1 g. per 
square cm., but at the bottom of the atmosphere, that is 
on the earth's surface, the pressure of an atmosphere 200 
kilometers or so in depth amounts to about 1 kg. per square 
cm. There are many simple proofs that 
the air exerts pressure. If a glass be filled 
by immersing it in a larger vessel of water, 
and then inverted and partly withdrawn, 
it remains full of water, although some of 
the water in the glass is above the level 
of that in the outer vessel. The pressure of the atmosphere 
on the surface of the water is transmitted equally in all 
directions. Inside the glass (Fig. 98) there is therefore an 
upward pressure far more than enough to support the water 
which fills it. If a hole be made in the up-turned bottom 
of the glass, air enters and presses the water within down 
to the level of that without. 

221. Take a glass quite filled with water. Cover it with 
a piece of writing paper a little larger than the top of the glass. 
Holding a flat smooth surface of board or pasteboard against 
the paper with one hand, grasp the glass with the other 
and quickly invert it. Now remove 
the pasteboard carefully. The paper 
will remain in place and the glass stay 
full of water. The force which sus- 
tains the water is due to the upward 
pressure of the atmosphere against 
the paper. 

222. Dropping Tube. If one end 
of a tube 3 mm. in diameter be dipped 
in water and the other closed with a 
damp finger, and the tube withdrawn 
(Fig. 99) , the tube will remain part full FlG - "--Dropping tube 
of water, held in by the upward press- an ^^ ette - 

ure of the atmosphere against the surface film at the bottom 
assisted by the surface-tension of the water. A pipette or 
a fountain pen filler illustrates the same point well. 




104 



GASES 



223. The pressure of the atmosphere is strikingly shown 
by the apparatus of Fig. 100. A piston fits in a cylinder 




Fig. 100.— Weight lifter. 

from the top of which the air can be 
exhausted. A piston 3 inches in diam- 
eter will easily lift 56 pounds. 

224. Torricelli's Experiment. Torri- 
celli, pupil of Galileo and member of 
the famous Florentine " Academy of Ex- 
periment/' devised a method of meas- 
uring the pressure of the atmosphere. 



Fig. 101.— Torricelli's 
experiment. 

He took a glass tube about a meter long, closed at one end, 
filled it with mercury, and closing the open end inverted the 
tube in a vessel of mercury. The tube did not remain full, 
but the mercury fell until the level in the tube was about 
76 cm. higher than that in the open vessel. 1 Torricelli con- 
cluded that the pressure of the atmosphere is equivalent to 
that of a column of mercury 76 cm. (about 30 inches) high. 
225. The force per square cm. at the bottom of such a 
mercury column is the weight of a column of mercury one 



1 The space above the mercury is called a Torricellian vacuum, 
contains nothing but a little vapor of mercury. 



It 



TORICELLI'S EXPERIMENT 



105 



cm. square and 76 cm. high (paragraph 162). The volume 
of such a column is 76 cc, and since the density of mercury 
is 13.6, its weight is 13.6 X 76 = 1033.6 grams. Every part of 
the surface of the mercury in the vessel must exert a pressure 
of 1033.6 grams per square cm. (about 14.7 lbs. per sq. inch), 
because the liquid transmits pressure equally in all directions 
(paragraph 157). The pressure at the free surface is balanced 
by that of the atmosphere, which must therefore exert a 
downward force of 1033.6 grams upon each square centi- 
meter of the surface of the mercury in the open vessel. 

226. Another explanation of the statement that the 
pressure of the atmosphere balances a column of mercury 
70 cm. high may be obtained by considering such an arrange- 
ment as that of Fig. 102. Suppose each arm of the bent tube 
one meter long and that it is half full of mercury. The stop- 
cock at S being open, the atmosphere 
presses equally on A and B, and they 
stand at the same level. If the stop- 
cock be closed, the level will still be 
the same, the air in the closed end 
exerting the same pressure as the 
atmosphere in the open end. If some 
air be withdrawn from C and the 
stopcock again closed, the quantity 
of air in C being less, the number of 
molecules per second striking against 
the surface B will be less, and B will 
rise, pushed by the greater pressure 
on A. If more and more air be withdrawn from C, the 
difference of level will increase, and if all the air could be 
extracted, B would stand about 76 cm. higher than A, the 
pressure of the atmosphere being balanced by the pressure 
of the 76 cm. of mercury alone. Now the surface A may be 
as large as we choose, and the conditions will change in no 
respect, and if C be contained within the other as in Fig. 103, 
the conditions would still be the same, and also the same as 
in Torricelli's experiment. 




Fig. 102 



106 



GASES 



227. Mercurial Barometer. Torricelli's apparatus, arranged 
in a case, with a scale by which the height of the column 
of mercury can be measured, is called the mercurial 
barometer (pressure-measurer). The 

height of the column, measured ver- 
tically, must be taken; not the length 
simply. If the barometer be tilted, 
the mercury will rise farther in the 
tube, and with an inclination of 20 
or 30 degrees from the vertical, the 
mercury will flow quite to the top 
of the tube. In accurate read- 
ings, corrections must be made for 
temperature, since warmer mercury 
being less dense than cooler, a given 
pressure will support a higher column 
of it. This may be easily observed 
by making simultaneous readings of 
two barometers on a cold day, one 
being in a warm room and the other 
out of doors. 

228. Before taking a reading it 
is necessary to see that the zero of 
the scale is at the level of the mercury 
in the reservoir. This is done in a 
variety of ways. One of the best is 
shown at the right in Fig. 104. The 
bottom of the mercury cistern is 
made of leather, and may be raised or 
lowered by the screw C. The ivory 
point a marks the zero of the scale, 
and the surface of the mercury may Fig. 104.— Barometer 
be brought to this with great accuracy an d cistern. 

by the screw. The pressure of the 
atmosphere varies from day to day and from place to 
place. It is commonly stated, not in grams per square 
centimeter, but in centimeters, millimeters, or inches of 




USES OF THE BAROMETER 107 

mercury. A pressure of 760 mm. of pure mercury at 0° C. 
is called one atmosphere, and in problems involving the 
condensing of gases, pressures are often stated in atmos- 
pheres. 

229. Uses of the Barometer. Any disturbance of the atmos- 
phere which heaps up more air than the average over a 
certain part of the earth makes the barometer stand higher 
there, and we say that winds tend to flow out of an area of 
high barometer 1 and toward an area of low barometer. A 
well-defined low area is called a storm centre. Rapid fall 
of the barometer in general indicates that a storm of some sort 
is imminent. Any comprehensive system of weather pre- 
dictions involves many other observations besides those of 
the barometer. It is often said that falling barometer 
indicates that the air is " light" because of water vapor in 
it. It is true that the presence of vapor of water in the air 
makes its density less, but the barometer shows nothing 
about either the density of the air or the quantity of water 
vapor in it. Air at 32° F. is about \ denser ("heavier") 
than air at 100° F., but the height of the barometer is not 
necessarily greater in cold weather. It is true that air is 
•made denser by increased pressure, but the atmosphere 
is subject to no pressure but that due to its own weight. 
It may expand or contract quite freely with changes of 
temperature without directly affecting the barometric 
pressure. 

230. A second use of the barometer is in determining heights 
above sea-level. Pascal was the first to show that the 
pressure of the atmosphere is less on mountains than at sea- 
level. In ascending 1000 meters above sea-level the barom- 
eter falls from 76 to 67 centimeters, an average of about 9 
millimeters fall for each 100 meters ascent. The following 
table gives barometric heights at 0°C. for each 100 meters 
up to 1100: 

1 This is the commonly used term for high atmospheric pressure. 



108 GASES 



ude (meters). 


Barometer (mm.) 


Altitude. 


Barometer. 





760.0 


600 


705.1 


100 


750.6 


700 


696-i3 


200 


741.2 


800 


687.6 


300 


732.0 


900 


679.1 


400 


722.9 


1000 


670.6 


500 


714.0 


1100 


662.2 




231. Aneroid Barometer. Let A be an air-tight metal box, 
with a large part of the air exhausted from it so that it will 
be in a state of tension, like a compressed spring, and the 
pressure within will be independent of temperature. The 
top is very thin and is corrugated so 
that it will not " buckle" as it rises 
and falls with change of pressure. 
Increase of atmospheric pressure 
makes the box thinner from c to d, 
and when the pressure decreases, the elasticity of the metal 
makes it spring out again. By an arrangement of levers, 
etc., this change of shape on the part of the box moves a 
hand in front of a dial. Such an instrument is called an 
aneroid 1 barometer. This form of instrument is easily carried 
about, and may be made very sensitive. Aneroids are 
much used, especially in determining altitudes. They must 
be compared with mercurial instruments in order to be sure 
that they are in correct adjustment. 

232. Boyle's Law. The relation of the volume of a mass 
of gas to the pressure on it has already been alluded to 
(paragraph 210). A bent glass tube (Fig. 106) affords a 
convenient means of experimenting on this relation. The 
short end, closed at c, must be of uniform bore, so that equal 
lengths shall have equal volumes. Mercury is poured into 
the open end and adjusted so that the level ab in the two 
arms is the same. The length of the air column in be is now 
measured, and this length measures the volume of the air 
in the tube, at a pressure of one atmosphere. If mercury 

1 Aneroid is from a Greek word meaning without liquid. 



DEVIATIOXS FROM BOYLE'S LAW 



109 



«U 



or 



u 



li 



i ii in 

Fig. 106.— Boyle's law 



be now poured slowly into the open end until it stands so 
that the height ba is equal to the height of the barometer, 
the air in be, which is the same mass of air as before, will 
be found to occupy one-half the space it did at first. It 
is now under a pressure of two atmos- 
pheres, the column of mercury ba being 
equivalent to one atmosphere, and the 
atmosphere itself still pressing on the 
mercury at a and through the mercury 
on the air in be. If in like manner 
the height ab be made twice the bar- 
ometric reading, the total pressure on 
the confined air will be three atmos- 
pheres, one of air and two of mercury, 
and the length of be will be one-third 
of its length when under one atmos- 
phere. In general, the volume occupied 
by a given mass of any gas, the tem- 
perature being unchanged, is inversely proportional to the press- 
ure upon it. A mass of air whose- volume at atmospheric 
pressure is 60 cc. will have a volume of 40 cc. at a pressure 
of one and a half atmospheres. This is the law of Boyle, 1 
independently discovered several years later by Mariotte. 2 

233. The fact expressed in Boyle's Law may be variously 
stated ; PV = a constant is one form, where V is the volume, 
and P the pressure on the gas or the pressure of the gas. 
We may also say: For a given mass of gas at constant 
temperature the density is directly proportional to the 
pressure. 

234. Deviations from Boyle's Law. Under very great press- 
ure all gases deviate from Boyle's Law. It may be true that 
the space not actually occupied by the molecules of gas 
does vary inversely as the pressure, and that when the 
total volume has been very much reduced the molecules 

1 Robert Boyle, 1627-1691, Irish chemist: made important additions 
to our knowledge of gases. 

2 Edme Mariotte, 1620-1684, French physicist. 



110 



GASES 



occupy an appreciable part of the remaining space, and since 
the molecules themselves do not become smaller, the diminu- 
tion now produced by added pressure is less in proportion. 

235. Flying. The subject of the resistance which the air 
offers to bodies moving through it has already been discussed 
(paragraph 92). Birds are able to support themselves 
upon the air because of its inertia. The wings move down, 
and the air is unable to escape immediately, so that by its 
reaction it supports the bird. The skill displayed by some 
large birds in sailing without moving their wings is the 
wonder and despair of the inventor of flying machinery. 
Aeroplanes, aerodromes, and tetrahedral kites are interesting 
subjects of study, but space for things so wholly experi- 
mental can hardly be afforded in a text-book. 

236. Wind as a Motive Power for ships has been in use 
since prehistoric times. The problem of how to sail a ship 
in any direction with the wind in any other direction is 
an interesting one, but the discussion is too long to be 
inserted here. The kinetic energy of the wind is also used 





Fig. 108. — Side view of wind-mill. 



Fig. 107. — Action of wind on vane. 

for driving machinery on 
land, through the agency of 
wind-mills. They are usually 
wheels with radial blades set 
at an angle of 45 degrees to 
the plane of the circumfer- 
ence. At right angles to this plane is a large fixed blade or vane 
which holds the wheel facing the wind. In the diagrams W 
shows the direction of the wind and A (Fig. 107) the direc- 
tion of motion of the vanes of the wheel. In countries where 
water power is scarce, wind-mills are used for grinding grain. 
In this country they are well adapted to pumping water for 
domestic use, since a reservoir holding several days' supply 



COMPRESSED AIR 



111 



insures against any inconvenience from occasional days of 
calm. 

237. Compressed Air is used for driving various kinds of 
machinery, particularly drills, and riveting and stone cutting 
machines. In mines and tunnels machinery is driven by 
the expansion of air compressed outside by steam or water 
power and sent into the mine or tunnel in pipes. The air 
thus serves both for power and ventilation. Compressors 
to be driven by power are made on the same principle as 
the force pump (paragraph 251). 

238. An important use of compressed air is in operating 
brakes on railroad trains and trolley cars. Air under 
pressure is sent into tunnels which are being constructed 
under water to keep the water from coming in. Some- 
times, where the material tunnelled is mud, the compressed 
air bursts out in a huge bubble and permits . the water 
to come in. A workman in one of the tunnels under the 
Hudson River at New York was caught in one of these bubbles 
and blown through many feet of mud and water and up 
into the air. He fell back into the river and was rescued, 
little the worse for his unique experience. In excavating 
for bridge-piers great boxes called caissons 

are sunk in the water and the water kept 
out of them by compressed air. Diving 
bells, for exploring the bottom in com- 
paratively shallow water, may be illus- 
trated by pushing a tumbler (mouth down) 
into water. 

239. The tires of bicycles and auto- 
mobiles are inflated with compressed air, 
which acts like the springs of an ordinary 
wagon, yielding to shocks and then ex- 
panding again, so diminishing the jolt to 
the rider. The plan of the ordinary 
bicycle pump is shown in Fig. 109. It consists of a 
cylinder C in which works a piston P, having a " cupped" 
leather with its edge turned down, held between two metal 



C 

Ae 



Fig. 109.— Bicycle 
pump. 



112 



GASES 



discs. When the piston is drawn up, the air from above 
it rushes past it, the edge of the cupped leather yielding. 
When the piston is pushed down, the edge of the leather 
is forced against the cylinder, so that the air cannot escape 
and is driven through the pipe A into the tire, where it is 
held by an inward opening valve. A similar pump, with the 
addition of a check-valve in the pipe A is used for inflating 
foot-balls and basket-balls. 

240. The Air-pump is used for exhausting air from vessels. 
It has many uses in connection with scientific experiments, 
and several in commercial operations. In sugar making the 
syrup is boiled under reduced pressure in " vacuum pans," 
the vapor being pumped off as fast as it is formed. Globes 
of incandescent lamps and Rontgen-ray tubes are exhausted 
by a special form of air-pump. 

241. Fig. Ill shows a form of air-pump now in common 
use for scientific experiments, and Fig. 110 shows its essential 
parts in section. The air is to be exhausted from the glass 
vessel R, called, curiously enough, a receiver. This vessel 
is fitted by means of a ground joint (and a little tallow) to 
the vacuum plate T. 
The stop-cock S being 
open and the inlet 
cock I closed, the pis- 
ton is pushed to the 
bottom of the cylin- 
der, the valve V t clos- 
ing and V 2 opening. 
The piston is then 
drawn up and on 
the first stroke V 3 
promptly opens, and the air above the piston is forced out 
into the outer air. On later strokes, V 3 does not open until 
the piston has gone up far enough to compress the air 
above it to atmospheric tension. When P is rising, the 
air in R expanding raises the valve V 1 and fills the cyl- 
inder. At each stroke the piston must be drawn all the 




Fig. 110. — Cross-section of air-pump. 



THE AIR-PUMP GAUGE 



113 



way to the top. Otherwise the air remaining above the 
piston expands as the piston descends and exerts pressure 
on V 2 , tending to hold it shut. On the down stroke, the 
piston must be pushed all the 
way to the bottom, otherwise 
the air left below it tends to 
hold V t shut. Air may be with- 
drawn from R so long as the air 
remaining in it exerts pressure 
enough to lift the valves. In 
order that they may be easily 




c^osstuv &.»«." 



Fig. 111. — Air-pump. 



lifted, they are often made of oiled silk, fitting over several 
small holes. Air pumps are made in which the valves are 
lifted mechanically instead of by the pressure of the air, 
thus enabling them to produce more perfect vacua. 

242. The Air-pump Gauge, shown at G, Fig. 110, is shown 
in detail in Fig. 112. G is a glass vessel, communicating 
with the receiver by the pipe 0, so that the air in the two will 
be at the same pressure. Within G is a U-tube closed at 
one end, the closed half being filled with mercury which 
extends around the bend. If it is intended for measuring 
the pressure at every stage of exhaustion, the arms of the 
tube must be 76 cm. long. They are commonly made about 
8 



114 



GASES 




Fig. 



112. — Air-pump 

gauge. 



16 cm. long, and the mercury stays at the top of the closed 
tube until about f of the air has been withdrawn from the 
receiver. When the mercury in the 
closed end stands 5 mm. higher than in 
the other, the state of affairs in the 
receiver is called "a vacuum of 5 mm." 
That is, the air in the receiver exerts 
pressure on the mercury in the open end 
of the tube sufficient to support a column 
of mercury 5 mm. high in the other side, 
upon which no pressure is exerted. This 
would mean that about j^-q- of the air 
which was in the receiver at the begin- 
ning remains there. 

243. Magdeburg Hemispheres. The first 
air-pump was made by Otto von Guericke, and his most 
celebrated experiment was tried before the Emperor of 
Germany at Magdeburg. He had pre- 
pared two metal hemispheres about 35 
cm. in diameter, fitting together air- 
tight. The air was exhausted from the 
sphere made by fitting them together, 
and the story is that four pairs of horses 
were hitched to each side, and were un- 
able to pull them apart. The original 
hemispheres are said to be preserved at 
Magdeburg. Pairs of Magdeburg hemi- 
spheres about 3 inches in diameter are 
furnished by instrument makers, and if 
they are well fitted, with a little tallow' 
between the edges, and thoroughly ex- 
hausted, a pull of nearly 100 lbs. is required to separate them. 

244. Oil-packed Air-pumps. A pump of the type described 
in paragraph 241 must be in very good working order to 
give a vacuum as high as 1 mm. The piston cannot fit 
quite accurately either at top or bottom of the cylinder, 
and air will leak in around the piston rod. Pumps are now 




Fig. 113.— Magdeburg 
hemispheres. 



SIPHOX 



115 



tfp 3 



T 



Fig. 114. — Mercury- 
air-pump. 



made in which the piston works in a heavy oil, and the 
valves are operated automatically. By arranging two 
such pumps in series, the second exhausting the space above 
the piston of the first, a vacuum of .001 of a millimeter 
may be obtained. Such pumps are now 
used for exhausting electric light bulbs 
and Rontgen-ray tubes. 

245. Mercury Air-pumps. For some 
purposes requiring high vacua, pumps 
are used in which the piston is replaced 
by mercury. One form is shown in 
the diagram Fig. 114. A vessel of mer- 
cury V delivers at B a succession of 
drops which fall down the tube T and 
carry between them bubbles of air from 
the bulb R. With such a pump vacua 
of one millionth of an atmosphere are 
readily obtained. 

246. Filter Pump. A large part of the air may be removed 
from a vessel by the apparatus shown in Fig. 115. A stream 
of water from the pipe P issues from the nozzle a with 
high velocity. The air in the space about the nozzle tends 
to adhere to the water and is carried by 
it through the pipe below. Such a con- 
trivance is used by chemists to hasten 
the flow of liquids through filters. A 
part of the air being exhausted from V, 
atmospheric pressure pushes the liquid 
through the filter. 

247. Siphon. In Fig. 116 M, the 
vessels .4 and B are filled with water to 
the same level, and are connected by a 
tube one end of which dips into each, 
and which is filled with water. The 
pressure of the air on the surface c, aided by the pressure of 
the column of water ed, tends to make the water flow from 
A to B, while the pressure of the atmosphere on d, aided 




Fig. 



115.— Filter 
pump. 



116 



GASES 




d[ 

N M 

Fig. 116.— Principle of 

siphon. 



by that of the column ec, tends to cause flow from B to A. 
In the conditions shown in M these forces are balanced and 
there is no flow. In Fig. N the column 
ed exerts greater pressure than ec, and 
therefore water flows in the direction of 
greater pressure. Water flows up ce, 
forced by atmospheric pressure on c, 
and down ed, against an equal atmos- 
pheric pressure on d, because of the 
difference of level between d and c. 

248. A customary form of siphon is 
shown in Fig. 117, a piece of rubber hose employed in draw- 
ing vinegar from a cask. In order to start the siphon it is 
necessary of course to fill it, which 

may be done in this case by holding ^ 
the hose in the position shown by the 
dotted lines and drawing it full with 
the mouth, and then closing the end 
and lowering it to the desired posi- 
tion. The liquid flows at because 
of the difference of level IB. 

249. The Common Pump is really a 
pneumatic machine, whose principle 
is like the air-pump described in 
paragraph 241. The piston P, Fig. 118, has an upward open- 
ing valve, and at the bottom of the cylinder is another, V. 
The piston is shown rising, withdrawing air from the pipe T, 
up which the water is starting, forced by atmospheric 
pressure on the water in the well. After a few strokes the 
water will flow into the cylinder and then the piston will 
lift water instead of air. 

250. The Duke of Tuscany had a deep well dug, and the 
pumps refused to work. Aristotle's philosophy said that 
the water rose from the well because Nature abhors a vacu- 
um. Plainly her abhorrence had limits! Galileo suggested 
that the pressure of the atmosphere forces the water up the 
pipe, and it must not be too high. Torricelli took up the 




Fig. 117.— Siphon. 



ROTARY PUMP 



117 



problem and solved it. The theoretical limit for standard 
atmospheric pressure is 34 feet, but in practice it is not 
satisfactory to have the distance from 
pump to water more than 20 feet. If 
the well is deep, the pump must be put 
some distance down in the well, and the 
water lifted the rest of the distance by 
the piston. 

251. The Force Pump is generally made 
with a solid piston, so that when it de- 
scends the water is forced through the 
valve V into the pipe T. The air- 
chamber A, as in the case of the hydraulic 
ram, is to secure a constant flow. By 
closing the cylinder at the other end, the 
piston rod sliding water-tight through a 
hole, intake and outlet valves may be 
put at each end. so that the pump delivers water on both 
strokes. Large pumps are generally thus made double-acting. 




Fig. 118.— Common 
pump. 





Fig. 119. — Force 



pump. 



Fig. 120. — Rotary pump. 



252. Rotary Pump. Where very large quantities of water 
are to be raised short distances, for irrigation or other pur- 
poses, rotary, or centrifugal, pumps are used. The plan of 
the common centrifugal pump is shown in the diagram. 
The water enters at the middle ^n one side. The paddle- 



118 GASES 

wheel revolves in a case and causes the water to whirl around 
and fly out at the outlet pipe, tending to leave a vacuum in 
the middle of the casing. Into this space water is forced 
up the supply pipe by atmospheric pressure. 

253. The Rotary Blower works on the same plan as the 
rotary pump. An old and familiar example is the grain 
fan for separating grain and chaff. The blower furnishes 
forced draft for fires, as for instance the blacksmith's forge, 
and air for heating and ventilating buildings and various 
other purposes. When the blower is used for ventilating it 
often takes out the used air instead of forcing in fresh. It 
is then called an exhaust fan. 

254. The Bellows, formerly used for starting fires in open 
fire-places and for blacksmiths' forges, is still employed for 
operating parlor organs and for some other purposes. 'A 
form used in laboratories to furnish air for blast lamps is 
shown in the diagram. To the 
bottom board, which is held 
up from the floor by feet, is 
hinged another board HK. 
The two being connected by 
a strong and flexible piece of 

leather, L. Above the upper „ 101 ~ ,. . / 

. .' , . . V , Fig. 121. — Cross-section of foot 

board is a strong piece of sheet bellows 

rubber R (shown distended); 

and in each board is an upward opening valve. A spring 
pushes up the top board, and it is pushed down by the pedal. 
The air is delivered at the exit E, the rubber membrane 
securing uniformity of flow. 

255. The Cartesian Diver (Figs. 122 and 123) named from 
its inventor Rene Descartes, the celebrated French mathe- 
matician and philosopher (1596-1650), illustrates the princi- 
ple of Archimedes, the transmission of pressure in fluids, the 
pressure of a liquid due to gravity, and the compressibility of 
gases. Nearly fill a small cylindrical vial or test-tube with 
water. Closing it with the finger, invert it in a glass of water. 
If it floats with some of the vial projecting above the water, 




THE CARTESIAN DIVER 



119 



Fig. 122 




Fig. 123. — Cartesian 
diver. 



take it out and put in more water. If it sinks, take out 
some of the water, and so by trial adjust it until it barely 
floats. The vial now floats because vial and air displace 
an amount of water equal in 
weight to the combined weight 
of the air and the vial. Clos- 
ing the opening with the finger 
transfer the vial to a deep glass 
jar with a narrow mouth. A 
quart or half gallon fruit jar 
will do, but a deeper jar is 
better. Now tie a piece of sheet rubber 
or bladder securely over the mouth of 
the jar. Slight pressure on the cover 
causes the air in the top of the jar to be 
condensed a little, exerting pressure on 
the water, which is communicated to the 
air in the vial, compressing it. The 
volume of the confined air being diminished, it no longer 
displaces a volume of water equal in weight to itself and the 
vial, so that the vial sinks. 

256. The compression of the air in the vial when it is 
about to dive in consequence of pressure on the cover can 
be distinctly seen. If the jar is deep and the buoyancy of 
the diver is adjusted with sufficient accuracy, it will stay 
down, and must be jostled to make it rebound from the 
bottom before it will rise. This is because the pressure due 
to the column of water in the jar keeps the bubble in the 
diver compressed so far as to keep it from floating. If 
after the apparatus has been adjusted the temperature 
falls a few degrees, the bubble will contract so much that 
the diver cannot be persuaded to float. If the top of the 
jar is small enough to be well covered by the hand, and 
the diver is well adjusted, it may be made to sink without 
any membrane, simply by dampening the palm of the hand 
and pressing it firmly on top of the jar. 



120 GASES 



EXERCISES AND PROBLEMS. 

1. A liter of air at 0° C. weighs 1.29 grams when the 
pressure is 76 cm. How much will a liter of air at 0° C. 
and 74 cm. pressure weigh? 

2. Why does a barometer give the same readings in the 
house as out of doors (at the same level and the same tem- 
perature) ? 

3. The capacity of a balloon is a thousand cubic meters. 
The weight of car, gas bag, etc., is 400 kilograms. If the 
balloon is filled with hydrogen, what load, approximately, 
will it carry? If filled with coal gas? 

4. The pressure of the atmosphere is about 1 ton per 
square foot. The area of a man's body is more than 10 square 
feet. Why are we not crushed by atmospheric pressure? 

5. In making high ascents, why do aeronauts sometimes 
suffer from bursting of the capillaries ? 

6. How high may the top of a siphon be above the level 
of the water in the upper vessel? 

7. When the barometer is at 76 cm., how high a column of 
water will the atmosphere support? The density of mercury 
is 13.6. 

8. Under the same conditions how high a column of sul- 
phuric acid (density 1.8) would be supported? 

9. What volume will be occupied by a kilogram of hydro- 
gen at 0° C. and 76 cm. pressure? By a kilogram of carbon 
dioxide ? 

10. Explain how the Cartesian diver illustrates all the 
points mentioned at the beginning of paragraph 255. 

11. Let 6c, Fig. 106, I, be 20 cm. If the barometer is at 
76 cm. and a be raised so that ab = 38 cm., how long will 
be be? 

12. Why do people often pour a little water into the top 
of a pump in beginning to use it? 



CHAPTER V. 

WAVE MOTION. 

257. Periodic Motion. The pendulum (paragraph 103) is 
a good example of periodic motion. It goes over the same 
or nearly the same path again and again in the same time. 
The periodic time is the time between two successive pas- 
sages through the same point in the same direction. Thus 
the periodic time of a pendulum is the time required for 
two swings. The periodic motion begins with a displace- 
ment from an equilibrium position. The force which causes 
the body to return to its former position is sometimes called 
the force of restitution. In the case of the pendulum the 
force of restitution is gravity. The inertia of the bob carry- 
ing it past the position of equilibrium produces a new dis- 
placement and so the motion continues. 

258. Variable Acceleration of Vibrating Bodies. It is evident 
that the pendulum bob moves more rapidly in the middle of 
its swing than when near the end, and that it must stop 
before it can swing in the opposite direction. The speed 
decreases gradually from the middle of the path toward the 
end and increases in the same manner on its return. The 
same is true of the end of a vibrating spring held in a vise. 
Here the force of restitution is due not to gravity but to the 
elasticity of the spring. In both these cases the decrease 
in speed is not uniform as is the case with a body thrown 
vertically upward, where we have the motion of the body 
opposed by a constant force. Here the force which opposes 
the motion of the body increases as the displacement increases, 
so that the farther the body travels the more rapidly does 
it lose speed. In the case of "the spring the reason for this 

( 121 ) 



122 



WAVE MOTION 




is evident, the force increasing as the displacement increases, 
according to Hooke's Law (paragraph 20). The force of 
restitution also increases with the displace- 
ment in the case of the pendulum because the 
farther it moves from the lowest position the 
steeper is the arc up which it moves against 
gravity. Resolve the force of gravity on the 
bob, G (Fig. 124) into a radial component R 
and a tangential component T. The former of 
these pulls against the string and the latter 
urges the bob along the arc. At the lowest 
position the tangential component is zero and it increases as 
the amplitude increases. 

259. Simple Harmonic Motion. If the motion be in a straight 
line and the force proportional to the displacement we 
shall have a kind of motion called 
Simple Harmonic Motion 1 (often 
abbreviated into S. H. M.). If a 
ball whirled at the end of a string 
be viewed from a distant point in 
the plane in which it revolves, it 
will appear to move 'in a straight 
line backward and forward. If A, 
Fig. 125, represents the actual path 
of the ball, to an eye in the plane 
of the paper the path would appear like B. If the ball 
revolve with uniform speed, the apparent motion back and 
forth will be simple harmonic. 

260. Definition of S. H. M. Let P v P 2 , P 3 , etc., in Fig. 
126 represent the positions at the end of equal periods of 
time of a point moving with uniform speed around the 
circumference of a circle, and A, B, C, etc, the corresponding 
positions of the foot of a perpendicular drawn from this 
moving point to a fixed diameter LK. Then as the point 
P revolves with uniform speed, the foot of the perpendicular 




The proof of this statement is beyond the scope of this book. 



GRAPHIC REPRESENTATION OF S. H. M. 



123 



moves back and forth along the fixed diameter LK with simple 
harmonic motion. The motion of the piston of a steam 
engine which is running uniformly is nearly S. H. M. With 
a device like that of Fig. 127 the piston would describe 
true S. H. M. The crank PC revolves about the centre C, 
and, with reference to the slot, the pin P also describes S. H. M. 

I 







Fig. 127 

The distance which the body moves in each direction from 
its middle position is called the amplitude of the S. H. M. 
In the case just cited the amplitude is the distance between 
the centres of P and C. 

261. Graphic Representation of S. H. M. Along a hori- 
zontal line AX, lay off a number of equal distances. At 



Fig. 128. — Simple harmonic curve. 

consecutive points erect perpendiculars proportional to 
OL, OA, OB, etc., of Fig. 126 respectively. (Fig. 128 is on a 



124 



WAVE MOTION 



scale t 3 q as large as 126.) For distances below the horizontal 
diameter of Fig. 126, place perpendiculars below the line 
AX. Join the extremities of these perpendiculars. The 
curve so drawn is a harmonic curve. The distances- along 
AX (called abscissas) represent times, and the perpendicular 
distances from AX (called ordinates) represent displacements. 



\N 



Fig. 129 




Fig. 130 



The displacements increase from zero at B to the entire 
amplitude at E, and then decrease to zero again at C. The 
time from B to D is one period. The shape of the curve 
depends upon the length of the abscissa chosen to represent 
a unit of time. It may be drawn of such a shape as Fig. 129, 
corresponding, so to speak, to slow time, or like Fig. 130, 
where the time spaces are longer, corresponding to fast time. 

Mechanical Tracing of Harmonic Curves. Fill a bottle with 
fine dry sand. Fit to it a cork, pierced with a small hole. 
Use the bottle (cork down) as the bob of a 
pendulum. While the pendulum is swing- 
ing draw under it in a direction at right 
angles to the motion of the bob (Fig. 131) 
a piece of paper coated with damp glue. 
The fine stream of sand will trace a simple 
harmonic curve on the paper. If the paper 
is drawn along slowly, the curve will have 
its loops crowded together like Fig. 129, and 
if it is moved more rapidly the curve will 
resemble Fig. 130. A bristle attached to a 
vibrating spring may in a similar manner be 
made to trace a harmonic curve on a piece of 
smoked glass or paper. Many other methods 
of producing such curves have been employed. 

262. Composition of Simple Harmonic Motions. 




Fig. 131.— Sand 
pendulum. 



The simplest 
trace given by a vibrating spring is of the type of Figs. 128, 



PHASE 



125 



129, and 130. If while it is swinging back and forth the 
spring is also changing its shape as it swings (quivering, so 
to speak, as well as vibrating), the curve may be like B, Fig. 
132. Here we have two simple harmonic motions taking 
place at the same time, and the resulting curve represents 
the sum of the two motions, a sort of resultant. Any 
number of simple harmonic motions maybe thus compounded. 




Fig. 132 

Let ABCD and AEFGC, etc., be two simple harmonic 
curves whose periods are to each other as 3 to 1 and the 
amplitudes are also as 3 to 1. By adding the corresponding 
ordinates. reckoning those below AX negative, we get a 
set of points, defining a new curve A HKL which is the 
result of compounding the other two, and represents the 




Fig. 133. — Composition of simple harmonic motions in the same plane. 

motion of a point constrained to describe simultaneously 
the two S. H. M.'s represented by the curves ABCD and 
AEFGC. This new curve is also periodic, having the 
same period as ABC. When the periods of the components 
are commensurable, the resultant curve is always periodic, 
but it does not necessarily have the same period as one of 
the components. 

263. Phase. If at the same instant two pendulums 
swinging side by side pass through their lowest point in the 



126 



WAVE MOTION 



same direction, they are said to be in the same phase; if 
they pass through it in opposite directions they are in 
opposite phase. In one case they are swinging together, 
in the other half a period apart. Phase is a relative 
term, referring to time since some instant chosen as the 
beginning of a period, and is most often used in practice in 
comparing two motions. Thus if we have two pendulums, 
one making three complete vibrations in six seconds, while 
the other makes four in the same time, and strike them at 
the same moment to start them into vibration, they will 
get farther and farther out of step, so to speak, until at 
the end of three seconds they are exactly in opposite phase, 
passing through the lowest point together in opposite direc- 
tions. At the end of the six seconds they will be together 
again in the same phase in which they started. The curves 
ABC and AEFGC in Fig. 133 are in the same phase at the 
times marked A and C, and in opposite phase at B and F. 
264. Composition of Simple Harmonic Motions at Right 
Angles. (I) When the period is the same. Suppose a 
body constrained to describe S. H 
with the amplitude OB, and also 
in the perpendicular direction CD 
with the same amplitude, and the 
same period. Suppose CD to ex- 
tend North and South and A B 
from West to East. If it start 
from eastward and at the same 
instant northward, the actual path 
will be OR, and the body will 
vibrate along the line RR'. If, 
however, the body start from A 
toward the north, it will describe a 
distance equal to OC in a quarter period, and a distance 
toward the east equal to AO in the same time, its velocity 
toward the north diminishing, and that toward the east increas- 
ing. The actual path described will be the quarter circle AC, 
and the complete path will be a circle. This circle represents 



M. in the direction AB 

XR 




Fig. 134. — Composition of 
simple harmonic motions at 
right angles. 



WAVES 127 

a phase difference of a quarter period, the body beginning 
a swing in one direction when it is in the middle of a swing, 
that is a quarter period ahead (or behind) in the other. 
The straight line FG is the path for a phase-difference of 
a half period if RR' be regarded as the path for like phase. 
Then a difference of J of a period would give the circular 
path again. Intermediate differences give ellipses. The 
one shown is the path for a phase-difference of \ and J of a 
period. All of these figures may be illustrated with a long 
pendulum. When the two amplitudes are not the same 
the circles will be replaced by ellipses. 

265. (II) Different Periods. Blackburn's pendulum, shown 
in Fig. 135 is a satisfactory apparatus for showing com- 
position of motions whose periods are different. It is 

supported at two points, C and D. = 

The whole pendulum can then swing 

at right angles to the plane of COD, 

and the part AO can swing in 

the plane of COD. The length of \£ 

the whole pendulum is AB, and the p IG 135 —Blackburn's 

part AO may be made any fraction pendulum. 

of AB that we choose. If AO = J 

AB its time of vibration will be § that of the whole pen- 
dulum, and the bob will swing from left to right and back 
while it makes one swing in the other direction. The bob 
will describe curves like one of those in the upper row of 
Fig. 136, the particular curve being determined by the phase- 
difference at the start. 

By varying the relative lengths of AO and AB an endless 
variety of figures can be produced. Fig. 136 shows two other 
of these, the ratio of the periods being 2 : 3 in the second row 
and 3 : 4 in the bottom row. 

266. Waves. When a gust of wind passes across a field 
of wheat, the stems bend and then spring back. Each 
stalk of wheat is in S. H. M., but because they are struck 
by the wind in succession, there is a difference of phase 
between successive stalks. As the wheat across the field 




12cS 



WAVE MOTION 



yields in succession to the force of the wind, a wave passes 
across the field. The stalks of wheat do not move across 



1:2 



2:3 




3:4 



Fig, 136. — Curves by Blackburn's pendulum. 

the field, but a form travels across, and this form is what 
we call a wave (Fig. 137). 

Water Waves. When a stone is thrown into still water 
a circular wave spreads out from the point where the stone 




Fig. 137 — Wave in wheat. 

struck. In this case the force acts at a particular point, and 
the wave is propagated by another force (gravity) called 



SPEED OF WATER WAVES 129 

into action by the initial disturbance. In the case of the 
wheat every stalk is acted on by the original disturbing 
force. If a single puff of wind strikes one side of a wheat 
field no wave passes across the field. At the point where 
the stone strikes, the water is pushed aside and heaped up 
around the stone. Gravity at once acts to pull down the 
displaced water, and the pressure which results disturbs 
the water beyond, pushing that into a heap, and so the 
action of gravity causes the wave to spread. 

A continuous succession of waves of nearly uniform size 
may be made by causing a vertical stick to move up and 
down in the water. Such a succession is called a train of 
waves. The highest part of the wave is called the crest, 
the lowest the trough. The distance (measured along a 
radius of the circular wave) from crest to crest is called the 
wave-length. 

267. Motion of Molecules of Water in a Wave. In deep 
water when a uniform train of waves is passing, the mole- 
cules of water near the surface describe circular paths with 
uniform speed. At a given point the motion of the surface 
is simple harmonic while a particle of water passes through 
the point in its circular path. Fig. 138 shows the paths of 




Fig. 138. — Motion of particles in water wave. 

thirteen molecules, each differing from the next in phase by 
■^2 of a period. The solid line joining points 1 to 13 shows 
the surface of the water at a particular instant, including one 
wave-length. The dotted line shows the surface J of a period 
later. The wave is moving from left to right. 

268. Speed of Water Waves. In deep water the speed of 
the waves increases with their length. Ocean waves may 
have a height of 30 feet or more from trough to crest and a 
length from crest to crest of several hundred feet. The 
speed of waves whose length is 200 feet is about 20 miles 
9 



130 



WAVE MOTION 



per hour. Such storm waves may travel a thousand miles 
or more out of the storm area in which they were produced, 
maintaining their length and speed but diminishing in height. 
As waves approach the shore and the water becomes 
shallow, friction against the bottom slows them down, and 
in water whose depth is much less 
than the length of the waves the 
speed depends only on the depth. FlG 139 

Thus the waves are crowded to- 
gether as they approach the shore, and if the beach slopes 
gradually the tops finally curl over and break. 

269. Refraction and Reflection of Water Waves. Another 
effect of this slowing up of the waves as they come into 
shallow water is to change their di- 
rection and make their crests more 
nearly parallel to the shore. Fig. 
140 shows a train of waves sweep- 
ing forward into water whose depth ( 
decreases uniformly, AB being the 
shore line, and CD, EF, etc., wave 
crests. This change of direction of N. \|i 
waves produced by retarding one N. 

part of them is called refraction. >P 

Waves which strike a nearly ver- FlG 140 

tical surface are reflected. This 

effect may be seen in a water trough by giving the water 
a push with the hand. A wave travels to the end of the 
trough and then comes back. 

270. Ripples. Surface tension as well as gravity tends 
to straighten out the surface of water when it has been 
thrown into waves. The surface film behaves as if it were 
stretched, 1 and in its effort to contract tends to keep the 
surface flat. The restraining effect of surface tension on 
waves more than 10 cm. long is so small as to be negligible, 
but in the case of waves 3 mm. or less in length it is the 

1 The surface film differs from an elastic body in that the force of 
restitution does not increase with the displacement. 




AIR-WAVES 



131 



predominating factor. These little waves are called ripples. 
A pencil thrust into the surface of a vessel of still water 
and drawn rapidly along produces ripples. Beautiful 
ripple effects are shown on the surface of water contained 
in a thin glass dish when a violin bow is drawn across the 
edge of the dish. In a shallow rapid stream ripples are seen 
where the water flows past stones and other obstructions. 

271. In contrast to gravitational waves, short ripples 
move more rapidly than long ones. Waves between 3 mm. 
and 10 cm. long are perceptibly influenced by both gravity 
and surface tension. Since surface tension has less effect 
on longer waves and gravity has more, there must be some 
wave-length between .3 cm. and 10 cm. which travels with 
minimum velocity. The length of these slowest water 
waves is a little less than 2 cm., and their rate about 23 cm. 
per second. 

272. Air-waves. When dynamite explodes, a quantity of 
gas is formed, and since the explosion occupies an incon- 
ceivably short time, the air is pushed aside to make room 
for the new gas not gently but with such violence as to com- 
press the air all around the point where the explosion took 
place. This condensed air at once ex- 
pands, and in doing so pushes the air next 
beyond, compressing that, and so a dis- 
turbance is propagated in all directions 
from the explosion. In this case the 
force of restitution called into play by 
the displacement is not gravitation but 
the elastic force of the air. 

273. A rapidly vibrating body, such 
as the prong of a tuning fork, sends out 
a train of air- waves. As it moves 
toward the right, Fig. 141, it compresses 
the air to the right of it and starts a 
condensation in that direction. As the 
prong moves toward the left it leaves a partial vacuum 
or rarefaction, which is at once followed by another condensa- 




Fig. 141 



132 WAVE MOTION 

tion. Thus a train of alternate condensations and rarefac- 
tions is sent out, one condensation and an adjacent rarefac- 
tion forming a wave. The distance from any point to the 
next point that is in the same phase is the wave length. 
It is convenient to think of it as the distance from the middle 
of one condensation to the middle of the next. 

274. Longitudinal and Transverse Waves. Water waves 
are said to be transverse, because the surface of the water 
moves at right angles to the direction of motion of the 
wave. The wave travels horizontally and the surface of 
the water moves up and down. A heavy body floating in 
deep water is moved up and down by the waves, but not 
horizontally. In air-waves the molecules move back and 
forth along the direction in which the disturbance is travel- 
ing. Such waves are longitudinal (lengthwise). When waves 
of this character travel through air or other gas, or through 
liquids or solids, as they may equally well do, the substance 
through which they move and whose elastic force propagates 
them is called a medium (plural media). A spiral spring 
serves well to illustrate longitudinal waves. If it is held 
stretched and plucked in the direction of its length, con- 
densations and rarefactions pass along it. A few scraps of 
white muslin tied to the spring at equal distances serve to 
make the vibrations more easily visible. 

275. Graphic Representation of Longitudinal Waves. A 
simple cross-section of the surface is manifestly the proper 
way to represent water waves. When we attempt to picture 



- 1 2 3 4 5 <3 r 8 9 10 1.1 1> 1,3 14 15 1<3 If 

J» * v \ \ #N > X * \ \ ' ' / >' '' / / i 

-rr ^i 4» h «♦ v ' N ** v «* ' •* V i* ** *^ *' **' ** *"' ** 

" B O 



A 

Fig. 142 



air-waves difficulties are presented. We may make a rather 
clumsy picture by means of a row of dots. In I (Fig. 142) 
the dots are equidistant, representing undisturbed particles 



SPEED OF LONGITUDINAL WAVES 133 

in a medium of uniform density. In II a train of waves 
is passing, some particles being displaced toward the right 
and some toward the left. The direction of motion of each 
is shown by the arrow. Particles 1 and 17 are in their normal 
positions, in the centre of rarefactions, and 9 is in its normal 
position in the centre of a condensation. Numbers 2 to 7 
are displaced toward the right and 10 to 16 toward the left. 
A more satisfactory picture of such a wave is made by draw- 
ing a horizontal line and laying off equidistant points along 
it, 1 to 17, and at each of these points erecting an ordinate 
whose length is equal to the displacement of the correspond- 
ing particle. Displacements toward the right are called 
positive and the ordinates placed above the line; those to 
the left are called negative and their ordinates are placed 
below the line. The ends of these ordinates being joined, 
we have the curve ABC which represents the conditions 
of the longitudinal wave in the same manner in which we 
have represented the harmonic motion of a single body. 
Any point of the curve shows by the length of its ordinate 
the amount of displacement at that point at that particular 
instant. 

276. Waves Transmit Energy. It is clear that a train of 
waves carries energy from the centre of the disturbance, since 
the medium is set in motion all along the path of the waves, 
and it requires energy to set matter in motion. The work 
done by the ocean waves in tearing down the shore in some 
places and building it up in others is evidence that waves 
possess energy. 

277. Speed of Longitudinal Waves. Since the force which 
is concerned in the propagation of longitudinal waves in air 
and other media is due to the elasticity of the medium, 
the greater the elasticity the greater will be the force called 
into play by a given displacement. Other things being equal, 
then, waves will be propagated more rapidly in a more elastic 
medium. All wave-lengths travel with equal speed. -The 
force which is pitted against the elastic force is the resistance 
to motion on the part of the medium, which we call its inertia. 



134 WAVE MOTION 

The mass of the medium which must be moved in a given 
distance increases with the density of the medium. It is 
evident therefore that the speed of propagation becomes 
less as the density increases. The speed of propagation 
of longitudinal waves in any medium is directly proportional 
to the square root of the elasticity of the medium and inversely 
to the square root of its density. This law is due to Newton, 
and is demonstrated in the Principia. 

278. Waves in Strings. If a stretched string be struck 
near one end, a transverse wave runs along the string, and 
on reaching the other end is reflected and comes back. The 
force of restitution here is of the same sort as that which 
propagates ripples on water. There, however, the force 
does not increase with the displacement, and in the case of 
the stretched string it does. All wave-lengths are trans- 
mitted with equal speed along the string, and the speed is 
proportional to the square root of the stretching force (ten- 
sion). When a part of the string is struck aside, the elastic 
force tends to pull it back and so make the string as short as 
possible, but in this process reaction pulls aside the next part 
of the string, and so the disturbance is passed along. A 
thicker string having greater inertia will respond less quickly 
to the force, and so the pulse travels more slowly along 
the heavier string. 

279. In experimenting with waves on strings it is well to 
use one along which they will travel slowly, so that the 
eye may follow them. This is most conveniently secured 
by using a heavy string, but a rope is apt to be too stiff to 
work well. A satisfactory substitute is a long rubber tube 
or a spiral spring one to two cm. in diameter and 5 meters 
or more in length. 

280. Interference of Waves. If two trains of waves meet 
in opposite phase they tend to neutralize each other. This 
effect is called interference. 1 Suppose the curved lines 

1 Some modern writers use the word interference to denote the effect 
produced by trains of waves meeting in any phase. 



STATIOXARY WAVES 



135 



of the diagram to represent the crests of sets of water waves 
from two sources, C and C . In the space where the two 
sets overlap, at the points marked X one set of waves tends 
to produce crests and the other to produce troughs. Inter- 




Fig. 143 



ference occurs at the points X, giving lanes of still water, 
while at the points the crests meet, and at points / 
troughs meet, making rough water along these lines. 

281. Stationary Waves. When waves moving along a 
string come to the end of it and are reflected, the reflected 
waves meeting the oncoming ones cause interference at each 
half wave-length from the end. At these points no motion 
of the string takes place, and they are called nodes. If the 
length of the string is any whole number of half wave- 
lengths it will continue for a time to vibrate in segments, 
forming a set of stationary waves, each wave having a node 
in the middle and at each end, and two vibrating segments, 
or as they are sometimes called, loops. Stationary waves 
may be set up in a long vessel of water by a properly timed 
disturbance. Columns of air are capable also of vibrating 
in stationary waves, and these, as well as those of strings, 
are of importance because they are so extensively used in 
music. Stationary waves are also of importance because 



136 WAVE MOTION 

of their employment in measuring wave-lengths. A single 
example is given in paragraph 317. 

282. Ether Waves, which are concerned in the phenomena 
of heat and light are transverse disturbances in the ether. 
The force which propagates them is electro-magnetic. They 
are capable of reflection and refraction and show the phenom- 
ena of interference. 

EXERCISE. 

Construct on coordinate paper two harmonic curves 
whose periods are to each other as 2 : 3 and their amplitudes 
as 1 : 2, and compound them by addition of ordinates, draw- 
ing the resultant curve. 



CHAPTEE VI. 



SOUND. 



283. Definition. Any disturbance capable of being per- 
ceived by our ears is sound. In general the disturbance is 
vibratory, because matter is elastic and disturbances tend to 
produce vibration. 

284. Media for Conveyance of Sound. In most instances 
the sounds which we hear are brought to our ears by trains 
of waves in the air. We say that air is a medium which 
conveys or propagates sound. A lady's fan disturbs the air, 
but because of its slow motion the air flows around it, being 
compressed to a degree too small to be measured. A bee's 
wing moves so rapidly that the inertia of the air prevents it 
from escaping, and so the strokes of the wing send out suc- 
cessive condensations and rarefactions forming a train of 
sound waves. Gases in general 
and also liquids and solids are 
capable of transmitting these 
trains of longitudinal waves. 

285. Vacuum Bell. The appa- 
ratus illustrated in the figure 
shows that sound is not trans- 
mitted across a vacuum. An 
electric bell B actuated by the 
battery cell C is suspended by a 
rubber band in the bell jar /, the wires passing through 
a cork covered with sealing wax to prevent the entrance of 
air. The bell can be heard quite distinctly, although the 
sound is somewhat muffled by the glass. If the air be now 
removed as completely as possible from the jar by means of 

(137) 




Fig. 144. — "Vacuum bell. 



138 



SOUND 



<m 



Fig. 145 



an air-pump, the bell can scarcely be heard. The little sound 
that we get comes chiefly through the wires and the rubber 
band, the rest through the air remaining in the jar. 

286. Sounding Bodies. Fig. 145 shows a piece 
of clock-spring secured in a vise. If the part of 
the spring above the vise is a foot long, it may 
be made to vibrate by drawing it aside, but gives 
no sound because the air flows around the slowly 
moving spring and no condensations or rarefac- 
tions are produced. If the spring be gradually 
shortened, it will when it is so short as to make 
about 30 vibrations in a second give a distinct 
sound. Fig. 146 gives an idea of the train of waves leaving 
each side of the vibrating spring. Each set forms a series 
of hemispherical waves, meeting 
in opposite phase and interfering 
in the neighborhood of the plane 
AB. If the source of sound be an 
intermittent jet of compressed air 
from a nozzle, we shall have 
spherical waves, since there will 
be no difference of phase on differ- 
ent sides. 

A vast variety of things may 
serve as sources of sound. Among 
those which give sounds of definite 
rates of vibration are metal plates and rods, stretched 
strings, wires, and membranes, bells, and columns of air con- 
tained in tubes. The tuning fork, much used in experiments in 
sound, is a modified rod, bent into the , 
form pi a U, with a handle attached. — )^ =nsni 

287. Limits of Hearing. The small- Fig. 147.— Tuning fork, 
est number of vibrations per second 

which constitutes a sound cannot be positively stated. It 
seems to depend on the character of the source and to be 
different for different persons. A large plate vibrating as 
slowly as 20 times per second seems to some observers to 




DISTANCES ESTIMATED BY THE SPEED OF SOUND 139 




Fig. 148.— Tuning fork on 
resonant case. 



give a definite sound. On the other hand, vibrations which 

are above a certain frequency are not audible. The limit in 

this direction also is different for 

different persons, but most of us 

cannot hear any sound from a body 

vibrating more than 20,000 times 

per second. 

288. The Speed of Sound in Air has 
been directly measured many times. 
In the open air at a temperature of 
0° C. it is about 332 meters (1090 
feet) per second. This speed in- 
creases with rise of temperature 
because air expands and becomes 
less dense when heated, while its 
elasticity is not changed. The speed 

is increased because of the decrease of density (paragraph 
277). Elasticity of air means simply its pressure. If con- 
fined air be heated, the elasticity is increased and the den- 
sity unchanged, but in free air rise of temperature causes 
expansion without change of pressure. The increase of 
speed is at the rate of about .6 meter per second per Centi- 
grade degree, or 1.1 feet per second per Fahrenheit degree. 
Change of atmospheric pressure does not affect the speed 
of sound, because pressure and density, by Boyle's law, in- 
crease and decrease together and in the same proportion. 

289. The Speed of Sound in Other Gases obeys the same 
laws. Hydrogen being only about -^ as dense as air the 
speed of sound in it is nearly j/15 times as great, about 
1275 meters per second at 0° C. 

290. Distances Estimated by the Speed of Sound. When 
a man is chopping wood, an observer at a distance often 
hears the blows when the axe is raised. Light moves 
with such inconceivable speed that we may say that the 
blow of the axe is seen when it occurs, while it is heard a 
second later at a distance of 338 meters if the temperature 
is 10° C. If a jet of steam is seen to issue from a locomotive 



140 SOUND 

whistle 5 seconds before we hear the sound, it is a little more 
than a mile away. 

291. The Speed of Sound in Liquids and Solids is, in general, 
greater than in gases, because their resistance to compression, 
that is their elasticity, is so much greater than that of gases. 
In water at 0° C. the speed is about 1400 m. per second. 
In wood (along the fiber) it varies from 3300 to 4600 meters, 
depending on the kind of wood. In rocks the average 
speed is about 4000 meters per second and in metals it varies 
from 17A0 for gold to 5000 for iron and aluminum. Ordinary 
rubber resists compression so feebly that sound travels 
through it very slowly, about 50 meters per second. It is 
not much more elastic than air and more than a thousand 
times as dense. 

292. Wave -Length and Rate of Vibration. The speed of 
propagation in a given medium is the same for sound of all 
wave-lengths, and if n = the number of vibrations per 
second, I = the wave-length in meters and v = the number 
of meters sound travels in a second, v = nl. If 50 freight 
cars each 8 meters long issue from a freight yard in one 
minute, the speed of the train is 8 X 50 = 400 meters per 
minute. When any two of the quantities n, I, and v are 
given, the other may be found. It is clear too that since 
for a given speed doubling n makes I half as great, the vibra- 
tion number is inversely proportional to the wave-length. 

293. String Telephone. The apparatus shown in Fig. 149 
is an interesting toy, and illustrates the propagation of 
sound by solids. Over the mouth-piece A is stretched a 
piece of parchment, to the middle of which is attached a 

TV # — {IT 

Fig. 149. — String telephone. 

string S, and at the other end of S is a duplicate of A. Speech 
uttered at A is reproduced at B, the string transmitting 
longitudinal vibrations throughout its length and setting the 
diaphragm of B in motion. By using a slender copper 



MEGAPHONES 141 

wire instead of a string, such a telephone may be operated 
successfully for distances up to 500 meters. 

294. Reflection of Sound. In common with all other known 
kinds of waves, sound may be reflected. The most frequently 
observed case of reflection is that of trains of waves travelling 
through air and meeting a solid surface. If the surface is 
large enough, and is nearly plane and vertical, and the 
source of sound not too close to it we get a clearly denned 
echo. Captains of steamers in the Norwegian fiords when 
surrounded by fog determine their distance from the cliffs by 
blowing the whistle and noting how soon the echo is heard. 

295. Whispering Galleries. Faint sounds made at certain 
points in the dome of the Capitol at Washington are distinctly 
heard at a corresponding point on the other side of the dome. 
This is caused by the curved surfaces reflecting the sound 
waves to a common point, or focus, and so concentrating 
the energy there. Such a dome is sometimes spoken of as 
a whispering gallery. Perhaps the most perfect example 
in the world is the elliptical dome of the Mormon Tabernacle 
in Salt Lake City. A pin dropped on a table at a certain 
point near one end of the great building can be distinctly 
heard more than 200 feet away at the other focus. 

296. Ear Trumpets used by persons whose hearing is im- 
perfect are sometimes cited as an example of reflection of 
sound. Their action is somewhat complex, and reflection 
plays a rather small part in it. They collect more energy 
than the ear alone can, and convey it to the ear. We some- 
times put a hand behind our ear to help in hearing faint or 
far away sounds. The hand does act as a simple reflector. 

297. Speaking Tubes, by which conversation can be carried 
on between distant rooms, simply confine the energy of the 
sound waves to a small space instead of permitting it to 
spread freely in all directions, causing more energy to reach 
the distant point than would otherwise reach it. 

298. Megaphones serve to direct the voice in a particular 
direction. The speaking trumpet, a long narrow trumpet 
formerly used for a like purpose, was far less efficient. In that 



142 SOUND 



case the air in the trumpet is set into vibration and the 
further end of it is the effective source of sound, the waves 





Fig. 150. — Speaking trumpet. 

spreading from that point in the same way that they would 
from the speaker's mouth. The broad flaring megaphone, 
however, sends much more energy in the direction toward 
which it is pointed than in a direc- 
tion at right angles to it. Lord 
Rayleigh 1 made this discovery in 
connection with apparatus to in- 
crease the range of sound from 

fog-horns, and he has given a Fig. 151 -Megapho^ 
mathematical explanation of it. 

299. Refraction of Sound. When aerial waves are reflected 
from a solid surface, nearly all the energy is reflected, unless 
the solid is a thin one so that its small mass is easily set in 
vibration. Then some of the energy will be communicated 
to the solid. If a train of waves encounter a medium of 
density only slightly greater than that through which it has 
been moving, but little reflection takes place, most of the 
energy passing on at a slower speed into the new medium. 
If the train of waves strikes the new medium obliquely, the 
retardation will have the effect of changing their direction. 
Imagine waves starting from A (Fig. 152) in warm air, and 
let CD represent the boundary of a region where the air is 
colder. The parts of waves which enter this colder air first 
travel more slowly, and the direction of motion is changed. 
Sound travelling along A in the warm air changes its direc- 

1 John William Strutt, Baron Rayleigh, 1842- . Brilliant English 
mathematical physicist. One of the discoverers of argon. 



TALKING MACHINES 



143 




tion to OB, and seems to be coming from A' '. This phe- 
nomenon is called refraction of sound. A clearly defined 
boundary between warmer and 
colder air would be very unlikely 
to occur. An irregular boundary 
causes the waves to be distorted 
and so broken up. 

300. Distant sounds are heard 
more distinctly when the air is 
uniform in density, proportion of 
moisture, etc., because this break- 
ing up of the sound waves will not 
occur. The air is apt to be more 
homogeneous at night than in the 
day time and on gray days than 
on fair ones, because when the 

sun is shining cloud shadows and various other causes 
make differences in the temperature of the air in different 
neighborhoods. It is a matter of common observation that 
distant sounds are heard more distinctly at night and in the 
still, cloud-mantled atmosphere which so often foretells the 
coming of a snow-storm. John Tyndall called these masses 
of air which break up and scatter sound "acoustic clouds." 
He describes a number of interesting experiments on this 
subject in his book "On Sound," which is perhaps the best 
popular treatise on sound in our language. 

301. Talking Machines. The first success- 
ful apparatus for reproducing the human 
voice and other sounds was the phono- 
graph, invented by Thomas A. Edison in 
1877. The plan of the original instrument 
is shown in Fig. 153. A diaphragm d, 
attached to a mouthpiece carries a stylus 
s which traces a line on the soft surface of 

the revolving cylinder C. In the original instrument this 
surface consisted of a sheet of tinfoil stretched over a spiral 
groove. When the diaphragm vibrates, the stylus instead of 




144 



SOUND 



/caving a smooth trace makes a groove full of elevations 
and depressions. When the stylus is made to retrace its 
path the diaphragm is forced to vibrate in the same manner 
that it did when the impression was made, and so reproduce 
the sounds which made the impression. 

302. Fig. 154 shows one of the earliest phonographs. It 
was turned by hand and the cylinder was carried forward 
by a screw cut on the left-hand end of its axle. In modern 




Fig. 154.— Phonograph. 

instruments the driving is done by some form of motor, 
and the impression is usually taken on a surface of hard 
wax. If copies are desired they are cast from hard rubber 
or other suitable material. 



PROBLEMS AND EXERCISES. 



1. A thunder-clap is heard six seconds after the lightning 
is seen. The temperature is 25° C. How far away was the 
flash? 

2. If one stand near a railroad track when a train is ap- 
proaching, the rails sometimes seem to make a clicking 
noise. Explain. 



PITCH 145 

3. Why are distant sounds likely to be heard more clearly 
across a body of water than at the same distance over the 
land? 

4. A distant explosion was noticed by the trembling of 
the earth and the rattling of windows. It was also heard 
through the air. Was the sound or the tremor perceived 
sooner ? 

5. Carbon dioxide is 1.529 as dense as air. Compute the 
speed of sound in carbon dioxide at 0° C. 

6. A boy holding his head under water hears a bell struck 
under water. If the distance is 200 meters and the tempera- 
ture 25° C, how long after the bell was struck does the 
sound reach the observer? (The velocity increases about 
.4 meter per second for each degree rise of temperature.) 

7. The very shrill sounds made by certain insects annoy 
some persons and do not disturb others. Suggest a reason 
for this. 

MUSICAL SOUNDS. 

303. Noise and Musical Sound. When each wave sent out 
by a source of sound is different from the last, as is the case 
when a pane of glass is broken or a cartload of stones emptied, 
we call the sound a noise. When, for an appreciable length 
of time, the waves sent out are similar, or when they are 
arranged in groups and the successive groups are similar, 
we have a musical sound. This definition does not imply 
that musical sounds always constitute music, or are always 
pleasing. They are sometimes discordant or otherwise 
annoying. On the other hand noises are sometimes pleasing, 
as the patter of falling rain and the rustle of wind-moved 
leaves. 

304. Pitch. In the case of comparatively simple musical 
sounds, one of their most important qualities is pitch, which 
depends upon the number of vibrations per second. If 
a toothed wheel be made to revolve with slowly increasing 
speed while a card is held against the teeth, we shall have 

10 



146 



SOUND 



at first a succession of taps. After a time the taps will 
blend into a musical note of low pitch, and as the frequency 
of the taps increases, the pitch of the note rises. Of course 
the length of the air waves sent out decreases as the frequency 
increases. 

305. The Siren. Reference has already been made {para- 
graph 286) to an intermittent stream of air as a source of 
sound waves. In the siren many simultaneous puffs are 
produced, so as to give a sound of considerable volume 
with low air-pressure. Fig. 155 shows a general view of 





Front view. 



Fig. 155. 



Back view, partly in section. 
-Siren. 



the instrument and a partial cross-section. Into the metal 
chamber air is forced by a bellows. It can escape by the 
diagonal holes. The wheel has the same number of holes 
as the air-chamber, sloping in the opposite direction. This 
wheel is pivoted so as to revolve very close to the top of 



LOUDNESS 147 

the air-chamber. The escaping air causes the wheel to re- 
volve. When it turns slowly the separate puffs of air are 
heard. As the speed increases these blend into a musical 
note, which rises in pitch as the speed is further increased. 
The actual number of vibrations per second may be deter- 
mined by means of the speed counter. This instrument 
shows pretty conclusively that pitch depends on vibration 
frequency only. Factory whistles are sometimes made in 
the same manner as the siren, and driven by steam. The 
same kind of a source of sound is sometimes employed 
for fog signals, placed on light-houses to be sounded when the 
light is obscured by fog. 

306. Doppler's Principle. If a source of sound is rapidly 
approaching an observer, the number of sound waves he 
receives per second is greater than the number sent out by 
the source, so that the pitch of the sound is raised by the 
approach of the source. Suppose the observer to be at B 
and the source of sound at 

A. During five seconds sup- - 4 > V -P 

pose A to send out 1000 air- Fig. 156 

waves and at the same time 

to advance to C, 332 meters from A. The observer will 
hear the sound during only 4 seconds, since one second will 
be saved in the time of transit of the last wave by the fact 
that it has 332 meters less distance to go than the first. 
Therefore the observer will hear 1000 vibrations in 4 seconds, 
or 250 per second instead of 200. In like manner, the pitch 
falls when the source moves away from the observer. These 
facts, known as Doppler's Principle, are well illustrated if 
a locomotive pass at a speed of 10 or more miles per hour 
with its bell ringing when one is standing close to the track. 
The pitch of the bell falls as it passes the observer. If the 
observer is on another train going in the opposite direction 
the effect is more conspicuous. 

307. Loudness of a sound, as we hear it, depends on the 
amplitude at the ear of the waves in the medium which 
transmits the sound to the ear, and on the density of the 



148 SOUND 

medium. Ordinarily, of course, these are air-waves. Loud- 
ness diminishes as the distance from the source increases. 
On mountain tops sounds are faint because of the rarity of 
the atmosphere. Strictly speaking, the air is a part of the 
sounding body, but we commonly restrict that term to the 
body whose vibrations are setting up air-waves. 

308. The amount of disturbance in the air depends on the 
amplitude of the vibrations of the source. This may be 
shown by means of a tuning fork mounted on a resonant case 
(Fig. 148). If it be lightly struck with a small rubber 
mallet, it gives a low sound. A harder blow causes it to 
vibrate with greater amplitude and the resulting sound is 
louder. 

The amount of energy communicated to the air also de- 
pends upon the size of the sounding body. If the tuning 
fork be detached from its box and held in the hand and 
then struck, 1 it will give a faint sound. If the handle be 
now touched to the table, the table becomes a part of the 
sounding body, vibrating at the same rate as the fork, and 
a much greater disturbance is made in the air. This experi- 
ment succeeds well with a table fork. 

309. Intensity. It is not possible to make any exact 
statements about loudness, because it is a subjective thing, 
a matter of judgment, based on sensation, and cannot be 
measured. The, intensity of a sound at a given point is a 
definite measurable thing. It is the rate at which energy 
is received at the point from the source in question. It 
might be measured in ergs received per second on one square 
centimeter at the place of observation. The intensity of 
sound from a given source is directly proportional to the square 
of the amplitude of the vibrations of the source, and if the sound 
is distributed in all directions in a uniform medium, the 
intensity is inversely proportional to the square of the distance 
from the source. 

1 A tuning fork should be struck upon something soft. A piece of 
soft wood does well, but sole4eather is better. 



MANOMETRIC FLAMES 149 

310. Quality. Sounds differ in other ways than in pitch 
and loudness. We distinguish the sound of a violin from 
that of a flute even though the same music be played with 
the same loudness. This difference is due not to the length 
of the air- waves nor to their amplitude, but to their form. 
A water wave may be complicated by smaller waves so that 
the outline of its curved surface is something like Fig. 157. 
In the same manner a train of sound waves may have 
smaller condensations scattered along among the larger ones, 
and this more complex series of waves produces upon the 
ear an impression different from that produced by the larger 
waves alone. These intermediate waves are heard as over- 




Fig. 157 

tones, and they are produced by vibrating ^bodies which 
instead of simple harmonic motion are executing several 
harmonic motions at once (paragraph 262). The differences 
in sounds due to the overtones present in them are called 
differences in quality. 1 The quality of a sound depends 
not only on the frequencies of the overtones present, but 
also on their relative amplitudes, so that we may have an 
endless variety of sounds in which the principal pitch is 
the same. The lowest pitch of which a vibrating body is 
capable is called its fundamental. This fundamental tone 
would give a train of waves of the simplest possible form, 
the addition of overtones giving more complicated forms. 
311. Manometric Flames. Konig, of Paris, maker of 
acoustic apparatus, invented a simple and ingenious method 
of studying the forms of sound waves. Fig. 158 shows 
the essential parts of the apparatus. A thin diaphragm, 

1 The French term is often used; it is timbre. The Germans say 
klangfarbe (tone-color). Some writers use the term character instead 
of quality. 



150 



SOUND 



which may be of rubber, divides the interior of the 
"capsule" into two parts. Gas enters by the inlet G, and 
escaping by a small jet forms a flame F. While the 
gas pressure is uniform the flame remains at a constant 
height. A pulse of air entering at A pushes against the 
diaphragm, increases the pressure in the left-hand compart- 





Fig. 158. — Manometric 
capsule. 



Fig. 159. — Manometric flame 
apparatus. 



ment, and increases the height of the flame. A succession 
of pulses causes the flame to flicker. When a sound is made 
at A, the flame flickers so rapidly that the eye cannot follow 
the changes, but every change of pressure affects the height 
of the flame. The apparatus is called a manometric (i. e., 
'pressure-measuring) flame. In order to render the flickering 




Fig. 160 



Fig. 161 



visible the flame is viewed in a revolving mirror. When no 
sound is made, the flame is seen because of the persistence of 
vision (paragraph 391) as a band of light across the mirror. 
But when a sound is made the band is broken into waves. 
In Fig. 160, A is the appearance when no sound is made, and 
B when a low note is uttered. If the note have an overtone 
whose period is half as great and its intensity half as great, 
we get such an effect as in A, Fig. 161, and if the sound be 



SYMPATHETIC VIBRATIONS 151 

a noise, the notches are irregular, as in B. Every variety 
of soun.d produces its characteristic curves in the mirror 
of the manometric flame apparatus, and we may say with 
truth that Konig's apparatus gives us pictures of sound 
waves, and illustrates to the eye what is meant by quality 
of sound. 

312. The Three Distinguishing Features of Sound are pitch, 
loudness and quality. Pitch depends only on the frequency 
of the vibrations, that is on the number of waves per second 
that strike the ear. Loudness depends in general on the am- 
plitude of the air-waves which reach the ear, and on the 
density of the air. Quality depends on the overtones which 
are combined with the fundamental, on the frequency of 
these overtones, and on the relative amplitude of all the 
tones of which the sound is made up. 

313. Forced Vibrations. When a pendulum swings freely, 
its time of vibration is determined by the force of gravity 
and by the length of the pendulum (paragraphs 107 and 
108). One may, however, take hold of the bob and move 
it back and forth more rapidly than its normal rate, or as 
slowly as he chooses. Such vibrations, in other than the 
natural period, and caused by an outside force, are called 
forced vibrations. The drum of the ear, the diaphragm of 
a telephone, and the thin wooden box of a violin or mandolin 
execute forced vibrations, vibrating in almost any period 
which is impressed upon them. The vibrations of the table 
mentioned in paragraph 307 are a good example of forced 
vibrations. 

314. Sympathetic Vibrations. If we attempt to swing a 
suspended body which weighs a hundred kilograms, we can- 
not make it swing slowly or quickly at our pleasure. By 
pushing it again and again and timing our pushes to suit 
the natural period of the pendulum, we may cause it to 
swing with considerable amplitude. When a child " works 
up" on a swing the same principle is illustrated. A small 
impulse repeated at each oscillation makes the swing move 
at last through an arc of almost 180°. Soldiers crossing 



152 SOUND 

a wooden bridge break step lest their rhythmic tread should 
cause dangerous vibration of the bridge. Other familiar 
instances of sympathetic vibrations might be cited. Many 
country children, for instance, have amused themselves 
by jumping in the middle of a log foot-bridge and causing 
it to yield more than it would with twenty people standing 
still on it. 

315. A striking illustration of sympathetic vibrations is 
shown by means of a pair of large tuning forks of the same 
pitch. One of them is supported on 
a box of thin wood, and the other 
having been set in vibration by strik- 
ing it on a pad is held as shown in the 
diagram. The other will presently 
vibrate powerfully. One air pulse 
would affect the stiff steel fork very 
little, but thousands of them exactly FlG ' ^^f^ 1 ^ 
timed produce a great effect. If we 

use forks whose rates are different by only one vibration 
per second the sympathetic vibrations will not be produced. 
If the loud pedal of a piano is depressed, so as to raise all 
the dampers from the wires, and a note sung into the space 
among the wires, one of them may be heard to respond with 
the same note which was sung. 

316. Resonance. Forced vibrations of boards and sympa- 
thetic vibrations of various kinds are called indiscriminately 
resonance, but the term is perhaps most often 
employed in a more restricted sense as applied 
to the sympathetic vibrations of columns of air. 
The diagram shows a column of air in a jar, 
above which is held a vibrating tuning fork. 
When the lower prong is moving downward a 
condensation starts down the jar. It travels F *^f 
to the bottom with the speed appropriate to the 
temperature of the air in the jar, is reflected and comes 
back. The prong in its upward journey sends a rarefac- 
tion down the jar in the same manner. If the vibrations 



RESONANT COLUMN FOR A NOTE OF GIVEN PITCH 153 




Fig. 164 



of the fork are properly timed so that the condensations 
and rarefactions follow each other up and down the jar, the 
air column will be set into vibration in stationary waves. 
The simplest form has a node at 
the bottom and a place of greatest 
motion nearly at the top. Using 
the mode of representing the air- 
wave described in paragraph 275, 
the length of the jar corresponds 

to a quarter wave-length, the distance from a node A to the 
next loop, B. If the jar be replaced by another 3 times as 
long, the column will have two nodes, and its length will be 
f of a wave-length, corresponding to the distance from A to 
D in the diagram. 

317. Resonant Column for a Note of Given Pitch. The 
apparatus shown in Fig. 165 illustrates the resonance of air 
columns very conveniently. T is a tube 2 or 3 cm. in 
diameter, placed in a tall jar of water. A 
tuning fork is set in vibration and held over 
the tube. By moving the tube up and down, 
the length of the air column can be varied 
at pleasure. By trial a position is found at 
which the air column resounds strongly, giving 
a sound whose total intensity is many times 
greater than that of the note given by the 
fork alone. The shortest length at which the 
resonance is strongest is almost one-fourth of 
the wave-length of the sound. The point of 
greatest motion of the air is at a distance 

beyond the end of the tube equal to about three-tenths of 
its diameter. A second point of strong resonance may be 
found if the tube is long enough, when the length of the 
air column is a half wave-length greater than at first. 

318. This experiment enables us to determine the speed 
of sound if we have a fork whose pitch is known. Suppose 
the vibration number of the fork to be 256, the tube to be 
2.5 cm. in diameter, and the shortest resonant column at 



Fig. 165 



154 



SOUND 



20° C. to be 32.85 cm. Adding the correction, .3 X 2.5 cm., 
we have 33.6 cm. as the quarter wave-length. The wave- 
length is therefore 134.4 cm. and the distance travelled in 
one second is the length of one wave multiplied by the number 
of waves sent out in a second, = 134.4 X 256 = 34406.4 cm., 
= 344 meters nearly. Reducing this to the zero value by 
subtracting .6 m. for each degree above 0° gives 344 — 
.6 X 20 = 344 — 12 = 332 meters per second as the speed 
of sound in air at 0° C. The length of the column when the 
next loud resonance is produced should be 32.85 cm. + \ X 
134.4 cm. — 100.05 cm. The point of greatest loudness is 
pretty sharply defined, a difference of a centimeter either 
way reducing the resonance to small fraction of the greatest. 
The boxes on which large tuning forks are mounted are 
called resonant cases, and they are made of such a length 
that the natural period of vibration of the air contained in 
them is the same as that of the fork. Sympathetic vibra- 
tion of the fork may be excited by holding a vibrating fork of 
the same pitch in front of the open end of the resonant case. 




Fig. 167 

319. Interference of 
Sound may be well shown 
by holding a vibrating 
tuning fork in front of 
the ear and turning 
it around. Suppose /, 
Fig. 166, to represent 
the ends of the fork prongs, approaching so as to make a con- 
densation between them while a rarefaction is starting from 



ORGAN PIPES 155 

and from 0'. The ear at A or B hears the sound of the fork, 
but at C the two sets of waves meet in opposite phase, inter- 
fere, and produce silence. A tuning fork held cornerwise 
over a resonant case as in B (Fig. 167) makes little sound 
because of interference. If it be held as in A, only one set 
of waves gets in, and resonance is produced. 

320. Beats. Most of the sound made by forks mounted on 
resonant cases is due to the vibration of the air in the cases. 
Such forks are best excited by means of a violin bow. If 
we have two whose pitch is the same and set them both in 
vibration we will in general get a louder sound than from 
one alone. By repeated trials it is possible to get them to 
vibrating in opposite phase, so that when one fork is stopped 
the sound is louder than when both are going. If now we 
put a small load 1 on one fork so that its pitch is lowered 
a little, and excite both, they will be alternately in the same 
phase and in opposite phase, so that the loudness of the 
sound will rise and fall. These periodic variations in in- 
tensity are called beats. The number may be increased by 
loading one fork more heavily, and in general the number 
of beats per second is equal to the difference in pitch of the 
forks. 

Organ pipes whose pitch is nearly the same give beats. If 
two consecutive piano keys near the lower end of the key- 
board are struck at once, beats are heard. 

321. Organ Pipes. When an air column is open at both 
ends and vibrating in the simplest possible mode it has a 
node in the middle and a loop at each end, the length of the 
pipe being a half wave-length of the sound, corresponding 
to the distance from B to D in Fig. 164. Such a column 
of air may be set in vibration in several ways. One of these 
is shown in Fig. 168. Air is forced into the triangular space, 
and escapes through a narrow slit at i against a sharp edge. 
The stream of air flutters, flowing first past one side of the 

1 A piece of beeswax stuck to one prong does well, or a piece of wood 
or wire shaped like a clothes pin, fitted to a prong. 



156 



SOUND 



edge and then past the other, and so sets the air in the 
pipe in vibration. This type, called the flue pipe, is used 




Fundamental note; § wave-length. 



£ 



First overtone, an octave higher than the funda- 
mental; whole wave-length. 



V ft ■ M 



Second overtone; 1§ wave-lengths 

Fig. 169 — Modes of vibration of air 

in open pipe; nodes at N. 

in church organs. By increasing the 
force with which the air is driven, the 
column in the pipe may be made to 
vibrate in parts, so as to give a note 
whose pitch is twice or three times as 
high as the fundamental, since the 
wave-length is \ or \ as great. 

322. In the closed pipe, the lowest 
possible note has a wave-length four 
times the length of the pipe, as with 
the resonant case. The closed pipe therefore gives a note 
having only half as many vibrations per second as the open 
one. Its overtones, as with the resonant column (page 153), 
have 3, 5, etc., times the frequency of the fundamental. 

323. The ordinary whistle, which 
country boys make from twigs of 
willow and chestnut is a small 
closed organ pipe. A tiny whistle 
in which the air column may be 
made as short as we please serves 
well to illustrate the upper limit of human hearing. As the 
column is shortened the pitch rises, and when the length 



Fig. 168.— Flue pipe. 



"^^ 



Fig. 170. — Lengthwise sec- 
tion of whistle. 



VIBRATION OF STRINGS IN PARTS 157 

is 2.5 mm., corresponding to about 30,000 vibrations per 
second, no sound is heard except the rush of the escaping air. 
Some observers can hear a shrill note when the length is 
3 mm., others cannot. This instrument is called the Galton 
whistle, from its inventor. 

324. Reeds. A reed is a slender tongue of metal so ar- 
ranged as nearly to close an opening in a metal plate. If it 
can vibrate without striking the sides of the opening it is a 
free reed. When air is forced against the reed it yields 
a little, and so nearly stops the flow 

of air through the opening. Then 
it springs back and repeats the per- 
formance. Such reeds are used in Fig. 171.— Vibrating reed, 
mouth organs, accordions, cottage 

organs, and many other instruments. The reed serves to 
set the stream of air in vibration, and the instruments are 
called reed wind instruments. A fish-horn has a reed w T hich 
strikes the opening and closes it, and then rebounds, produc- 
ing a discordant note. The clarinet and oboe have striking 
reeds. 

325. Vibrating Strings. When the violinist in tuning his 
instrument wishes to raise the pitch of a string he tightens 
it, or if it is too high he loosens it. The piano maker uses 
heavy and long wires for the low notes and thin short ones 
for the high notes. If strings were perfectly flexible, so that 
their rate of vibration would not be influenced by their stiff- 
ness, their pitch would follow these three laws: 

(1) The pitch of a vibrating string is inversely proportional 
to its length; 

(2) directly proportional to the square root of the stretching 
force; and 

(3) inversely proportional to the square root of the mass 
per unit length. 

326. Vibration of Strings in Parts. If a string be stretched 
on the sonometer, Fig. 172, and plucked with the ball of the 
thumb half way between the bridges it will give its funda- 
mental tone, vibrating as a whole. If now it be damped 



158 



SOUND 




Fig. 172. — Sonometer 



in the middle by holding a finger against it, and plucked 

in the middle of one half, the string will vibrate in halves. 

These are stationary 

waves, and the length 

of the string is now one 

wave-length. When it 

vibrates as a whole the 

stationary wave is only 

a half wave-length, and 

the note has half as many vibrations per second as when 

it vibrates in halves. 

327. If the string be damped so that one segment is twice 
as long as the other and plucked in the middle of the shorter 
segment, it will vibrate in thirds, and give a note whose 
vibration number is three times as great as at first. These 
modes of vibration and many more may all exist at once, 
causing the string to vibrate in very complex waves, giving a 
note having many overtones and therefore complex quality. 

328. The mode of setting a string in vibration determines 
to a large extent whether or not the resulting sound shall be 
rich in overtones. The violin bow, covered with powdered 
rosin, sticks for an instant to the 
string, and when it has drawn it 
aside a little way the tension of 
the string pulls it back; then the 
bow takes hold again and so on, 
setting the string in vibration. 
This mode of exciting a string 
gives a brilliant sound, that is, 
one having many overtones. 

329. Nodes in Vibrating Plates. 
If a square plate of metal or glass 
be held in the middle by a screw 
or clamp, it may be made to vibrate 
by bowing the edge with a violin 
bow. While one part of the plate 
is moving up an adjacent part Fig. 173.— Sand figures. 













7 


^ 


^ 


r 




\ 


/ 


/ 


\ 




X( 




ACCESSORY VOCAL ORGANS 159 

will be moving down, and vice versa. The line between 
these vibrating segments is at rest and is a node. If a little 
sand be spread upon the plate it settles upon the nodes, 
forming a figure showing the mode in which the plate is 
vibrating. This experiment is due to Chladni, an Italian 
philosopher. Some of the figures which may be easily 
obtained are shown in Fig. 173. 

If, while the plate is vibrating, the hand be held close 
over one segment the sound is much louder because of the 
cutting off of a part of the interference. 

330. Voice. The vocal cords are two membranes contained 
in an enlargement of the wind-pipe called the larynx or voice- 
box. This enlargement shows in men's throats as the 
Adam's apple. When not in use the vocal cords lie against 
the sides of the larynx. When in use they are drawn tight 
by special muscles, so as to leave a narrow slit through which 
the air passes and sets the cords in vibration. The pitch 
of the sound depends, as in the case of vibrating strings, 
on the length, weight, and tightness of the cords. It also 
depends on the length of the air column above the cords. 
When we wish to utter a very low note, we loosen the cords, 
depress the larynx, and thrust the lips forward. When we 
utter a high note we tighten the cords, push up the larynx, 
and draw back the lips. Women's voices average much 
higher in pitch than men's. This is due to the vocal cords 
of women being both thinner and shorter than those of men. 
The shorter cords are contained in a smaller larynx, and 
the Adam's apple is not conspicuous in women. 

331. Accessory Vocal Organs. The tongue, lips and teeth 
and the nasal passages modify the sounds made by the vocal 
cords in various ways. The cavities of the throat and nose 
are of special interest because the individuality of the voice 
depends chiefly on their shape. No two persons have features 
exactly alike, so that we should know our friends if we 
unexpectedly met them in Madagascar. So no two persons 
have air passages of the same shape. Any two voices 
will therefore contain differently related overtones, and 



160 SOUND 

entirely aside from any tricks of speech or peculiarities of 
pronunciation each person has his own voice, unlike any 
other. Family resemblances in voice, so often noticed, are 
due to likeness in the shape of the air passages. 

332. The Ear. The external organ called the ear serves 
in the case of horses, cats, and some other mammals the 
same purpose as the ear-trumpet. Man's external ear is 
so flattened against the head as to be of little use. A slightly 
crooked passage leads to the drum or tympanum, a tough 
membrane closing the middle ear, in which is a chain of bones 
one end of which rests against the drum and the other against 
a membrane which closes the passage of the inner ear. The 
drum is set into vibration by air-waves and sets the chain of 
bones in motion. They in turn carry the impression to the 
inner ear, which consists of a spiral chamber filled with 
liquid. In this spiral chamber is arranged the mechanism 
which gives the impression of sound to the auditory nerve. 
The nerve of hearing terminates in a series of bristles of 
varying length floating in the liquid of the inner ear. This 
set of bristles form the organ of Corti. It was long supposed 
that the nerve termini are set into sympathetic vibration 
by the vibrations of the liquid. The bristles are each at- 
tached by one end to the edge of the basilar membrane, 
which varies in width and is stretched in the direction of its 
breadth, the shorter bristles being attached to the narrower 
part of the membrane. It is now believed that it is this 
membrane which is set into sympathetic vibration by the 
disturbances of the liquid, a narrower part responding to a 
sound of high pitch, and a broader part to one of low pitch. 
The vibration of any part of the membrane disturbs the 
nerve termini connected with that part, and so we are able 
to distinguish the note or notes which a sound contains. 
If a sound contains two distinct notes, almost any one can 
hear them both if their intensities are nearly equal. A 
highly trained ear can distinguish a considerable number of 
harmonics blended together, even if their intensities are very 
different. If four persons are singing together it is generally 



DIATONIC SCALE 161 

not difficult by an effort of attention to hear the voice of 
any one of the four. The power of analysis possessed by the 
ear is perhaps best illustrated by our ability to listen to 
one person and understand him perfectly when four or 
five persons are saying different things at the same time 
with nearly equal loudness. 



MUSICAL SCALES. 

333. Musical Interval. The musician defines musical inter- 
val as the difference in pitch between two notes. It is not 
a difference obtained by subtraction, but by division. It 
is the ratio of the frequencies of the two notes. If one note 
has 256 vibrations per second and another 320, the interval 
between them is 320 h- 256 = f . 

334. Diatonic Scale. Two notes whose fundamental 
pitches are the same, however they may differ in quality 
and intensity, harmonize when sounded together. So do 
many other combinations, and those notes whose vibration 
numbers have the simplest ratios harmonize best. This fact 
was discovered by the ancient Greeks, and is explained in 
paragraph 338. The ratio T is of course the simplest 
possible, and the next in order of simplicity, excluding those 
whose value is greater than 2, are f, -§ , -§-, f, and f . If we 
arrange a series of six notes so that the second has -f as many 
vibrations per second as the first, the third -f as many, the 
fourth -| , the fifth f, and the sixth twice as many as the first, 
all of these will harmonize with the first and most of them 
with each other. If the first note has 24 vibrations per 
second, the series of six will be as follows: 24, 30, 32, 36, 40, 
48. The most inharmonious pair in the group is made up 
of the second and third notes, whose interval is yj-. Be- 
tween the first and second and between the fifth and sixth 
notes the intervals are much greater than between the. other 
consecutive notes. In these places additional notes are 
inserted, making a series of 8 notes called an octave (Latin 

11 



mi 


fa 


sol la si 


do 


5 

4 

30 


4 
3 

16 

T5 

32 


3 5 15 
2 3 8 
9 10 9 
S IT 8 

36 40 45 


2 

16 

T5 

48 



162 SOUND 

Octo, eight). In the first line of the table below are shown 
the names of these notes as given in vocal music, in the 
second line the intervals between each note and the first 
of the octave, in the third the intervals between consecutive 
notes, and in the fourth the smallest whole numbers which 
are proportional to the frequencies of the notes of the octave. 

do re 

1 -2- 

1 8 

9 10 

"8 ~9" 

24 27 

The actual pitch of the first note may be anything whatever, 
but the seven notes which follow it must have the above 
ratios to it and to each other. The series of 8 notes related 
in this way is the diatonic scale, often called simply the scale. 

335. Intervals of the Scale. Half Tones. All the intervals 
within the octave are named : ^~ is called a minor tone and 
f a major tone. Because the third note of the diatonic scale 
has f the frequency of the first, the interval £ is called 
a third. For a like reason f is called a fourth and f- a fifth. 
When a violin is " tuned in fifths" each string vibrates 1^- 
times as often as the next lower. The interval -f- is called 
an octave, and the note whose frequency is twice as great 
is the octave 1 of the other. Five of the intervals between 
successive notes of the scale are either major or minor tones, 
not very unequal. The other two, between mi and fa and 
between si and upper do are much less. In the five large 
spaces half notes are inserted, making a scale of 13 notes 
called the chromatic scale. 

336. Repetition of the Scale. The last note of the scale 
has the same name as the first, and forms the first note 
of a second octave, in which the notes have the same 
relation to each other as in the first. On a piano, or any 
other instrument in which the performer does not vary 

1 It will be observed that the word octave has three distinct but 
closely related meanings. 



EQUALLY TEMPERED SCALE 163 

the pitch of the strings at will while playing, the number of 
keys must be as great as the number of notes required. The 
lowest note of a modern piano is called A and has a frequency 
of about 28 vibrations per second. The third white key, 
C, is regarded as the first note of an octave, so that white 
keys C, D, E, F,G, A, B,C give notes corresponding (nearly) 
to those of the diatonic scale. Black keys are inserted 
corresponding to the half notes of the chromatic scale. The 
second C begins a new octave and so on. The whole number 
of octaves is 7^, counting 12 notes to an octave. Three are 
below the first C and the highest note is C, making 4 beside 
the seven octaves. The black keys are called sharps and 
flats. The note between A and B is either A sharp or B flat. 

Key Note. In vocal music the octave always begins with 
do, but do may have any pitch whatever. On the piano 
if we start with any other note than C and strike 8 white 
keys they will not form an octave, because the intervals 
will not be correct. By using both black and white keys, 
properly selected, an octave may be made up, beginning 
with any key we choose, but such an octave will be only 
approximately correct. A series of octaves beginning with 
any other note than C is designated by the note with which 
it begins, as "Key of F," etc. 

337. Equally Tempered Scale. No arrangement of the half 
notes will permit all the octaves picked out as described in 
the last paragraph to be absolutely correct. Various modes 
of reducing the errors have been employed. This process 
is called temperament. The method now universally em- 
ployed in pianos is to adjust all the intervals between ad- 
jacent keys to the same value. This scale is called the 
equally tempered scale, or simply the tempered scale. The 
value of the interval is easily computed. Suppose the 
first note of an octave to have 264 vibrations, and let x = the 
common ratio. Then the second note has 264rc vibrations, 
the third 264r\ etc., the thirteenth having 264x 12 , which must 
equal 2 X 264. Therefore x 12 = 2 and x = y'2 = 1.0594 
nearly. In the diagram is shown a string with the points 



164 SOUND 

where the bridge must be placed to make the notes of the 
diatonic scale, and on the other side the points for the 

For diatonic scale. 



D E F G A EC 

I i 'i I i 1 i ', , 1 1 



For equally tempered scale. 

Fig. 174. — Division of the string to give notes of the scale. 

equally tempered chromatic scale. It will be seen that 
several of the notes of the two scales are not exactly alike. 

Equally tempered chromatic scale. 



V* E b G b A b B b D b JS b G b A b 2 b J) b Z b 

Movable selector for finding the notes of 
any key; now set for B flat. 

Fig. 175 

Fig. 175 shows an' arrangement which may be made of 
pasteboard to show how the notes of any key are selected 
from the equally tempered scale. 

338. Harmony and Discord. If several notes are sounded 
•together, the effect produced is sometimes pleasant and 
sometimes unpleasant. The former effect is called harmony 
and the latter discord. When two notes differ by -^ of a 
vibration per second or less, so as to give very slow beats, 
the effect is not very unpleasant, but if the number of beats 
per second be from five to ten, the rise and fall in the loudness 
of the sound produces a very unpleasant effect on the ear. 
The notes are discordant. They affect the ear in much the 
same way that the flickering of a light affects the eye. 
If the flame rises and falls from five to ten times per second, 
the effect, if the light be intense, is very painful. If, however, 



PROBLEMS AND EXERCISES 165 

the light flickers 50 times in a second, it appears entirely 
steady, since the eye does not perceive its variations because 
of the persistence of vision, alluded to in paragraph 391. 
The ear behaves in the same way. When the mechanism 
of hearing has been set in motion it continues in motion for 
a small fraction of a second, and if a second impulse comes 
before the first has begun to fade, the sound seems con- 
tinuous. Discord is caused by beats, but if the beats are 
sufficiently numerous the effect is not discord but harmony. 
The number of beats per second required to produce maxi- 
mum discord, and also the number required to produce 
harmony, is greater in the case of sounds of higher pitch. 
This is perhaps because the parts of the organ of Corti which 
respond to sounds of higher pitch remain in vibration a less 
time when they have been excited. 

339. We have now the explanation of the fact discovered 
by the Greeks, that those notes are most harmonious whose 
vibration numbers have ratios represented by the smallest 
whole numbers, or as we may say more briefly, whose 
intervals are the simplest. The most harmonious combina- 
tions are 1 : 1 (unison); 2 : 1 (octave); 3 : 2 (fifth); 4 : 3 
(fourth); and 5 : 4 (third). All of these are found in the 
diatonic scale. Three notes whose rates are to each other 
as 4 : 5 : 6, as do, mi, and sol, form what is called a major 
triad or major chord, a particularly harmonious grouping. 
All of these combinations are such that the number of beats 
per second is very rapid and therefore they are harmonious. 
In the middle octave if C is 264, E 330, and G 396, the smallest 
number of beats per second is 66, which is entirely imper- 
ceptible to the ear. 

PROBLEMS AND EXERCISES. 

1. A siren wheel has 22 holes and makes 630 revolutions 
per minute. What is the pitch of the note? 

2. A bicycle is moving at the rate of 10 meters per second, 
and its bell is making 340 vibrations per second. The 



166 SOUND 

temperature is 30° C. How many vibrations per second 
does a stationary observer hear when the bicycle is directly 
approaching him ? When it is receding ? 

3. Why does a long ship rock less than a short one? 

4. Middle C of concert pitch makes 272 vibrations per 
second. Determine the number for the other notes of the 
diatonic octave. 

5. A of a certain scale has 435 vibrations per second. 
Determine the number for each note of the octave. 

6. Two tuning forks beat once in 3 seconds. How could 
you tell which has the higher pitch? 

7. At a temperature of 20° C. the shortest resonant 
column for a certain fork is 19.17 cm., with a tube 2 cm. in 
diameter. What is the pitch of the fork? 

8. An open organ pipe has an air column 70 cm. long. 
How long a column should a closed pipe have to give a note 
an octave higher? 

9. A violin string 50 cm. long gives middle C. How long 
a string of the same thickness and tightness will give A? 

10. Two strings of the same length and thickness are 
stretched with forces of 4 and 9 lbs. If the former gives 
200 vibrations per second, how many does the latter give? 



CHAPTEE VII. 

LIGHT. 

340. Definition. Sources. Light consists of such disturb- 
ances of the ether as are perceived by the eye. The disturb- 
ances seem to be caused by vibratory motion of the molecules 
of matter. Any body in which such vibrations are going 
on communicates disturbances to the surrounding ether, and 
if these disturbances are of such frequency as to affect the 
eye the vibrating body is called a source of light. Most 
familiar sources of light also give out the longer waves which 
we call heat. The sun, burning materials generally, and the 
carbon of an incandescent lamp are hot as well as bright. 
Some insects have light-giving organs which give out almost 
cold light, and decaying wood sometimes gives a so-called 
phosphorescent light almost without heat. 

341. The Nature of the Disturbance of the ether has been 
mentioned in paragraph 282 and will be further discussed in 
Chapter XII. For the present it will be sufficient to say 
that the waves are now believed not to involve any actual 
motion of the ether, but the moving through it of an electro- 
magnetic disturbance which involves change of condition 
but not change of place on the part of the ether itself. We 
shall call these disturbances light waves. 

342. Light a Form of Energy. Light is absorbed by many 
bodies and heats them, and heat is a form of energy, since it 
can be made to do mechanical work. These facts which 
will be discussed later give some hint of the evidence on which 
is based the belief that light is a form of energy. 

343. Media. Light waves are, we believe, always ether 
waves. Ether is therefore in the strict sense the only medium 

(167) 



168 LIGHT 

for the propagation of light. The ether is supposed to 
exist among the molecules of substances, and those sub- 
stances which permit light waves to pass through them are 
called media. Air and other gases, water and many liquids, 
glass and some other solids are media, and if like those 
mentioned they permit the passage of trains of waves 
without breaking them up, the substances are transparent. 
A transparent medium is one through which it is possible to 
see objects distinctly. Such substances as thin paper and 
ground glass, which permit light to pass, but through which 
we cannot distinguish objects clearly are translucent. The 
trains of waves are broken up and scattered in passing 
through. Objects through which light does not pass, such 
as metals and most solids, are opaque. Thin slices of 
opaque substances are often translucent. A single sheet 
of paper may be translucent, while fifty sheets together 
would make an opaque body. Some light falling upon the 
pile of sheets of paper would penetrate the first sheet, a 
part of that which passed through the first sheet would also 
pass through the second, and so on. Thus light penetrates 
to a certain extent the surfaces of some opaque bodies. 
Most of that which penetrates is absorbed and heats the body. 
344. Emission Theory. Newton believed that light con- 
sisted of exceedingly minute particles shot out by the 
luminous body. One reason for rejecting the wave theory 
was that it makes necessary the assumption that a medium 
fills the interstellar spaces, since we could not otherwise 
receive trains of waves from the sun and stars. Another 
reason which influenced Newton is the fact that light seems 
to travel in straight lines, and not to bend around corners 
as sound waves do. Suppose a train of sound waves coming 
out of a building by the passage P (Fig. 176). When a con- 
densation has reached B, the air in this condensation expands 
so as to push not only the air in front of it, but also to a less 
degree that at the sides, so that waves are sent in all direc- 
tions, observers at A and C hearing the sound, but not so 
loud a sound as an observer at D. If a train of light waves 



SHADOWS 



169 



came through the passage, they would fall upon the ob- 
server at D, but not at all upon those at A and C. Light 
does in fact to a very small 
extent bend around the 
corners of obstructions (para- 
graph 436), but this was not 
known in Newton's time, and 
so he rejected the wave theory. 
Fresh interest attaches to the 
emission theory since the 
discovery of radioactivity, 
because radium and some 
other substances do send out 
streams of particles which 
suggest Newton's corpuscles. 
345. Shadows. If an opaque 
body be placed between a source of light and a surface upon 
which the light is falling, some of the light is intercepted, 
and a shadow is formed on the illumi- 




Fig. 176 



A, 






ii 



£:- 



\ 



\ 



\ 



&\ 



Fig. 177 



nated surface. If the source of light 
be small and the opaque body close 
to the surface, the shadow is sharply 
defined. Suppose a source of light 
at A, indefinitely small, and an 
opaque object BC casting a shadow 
DE on a wall. If there were no dif- 
fraction (paragraph 436) the shadow 
would be sharply denned, a point 
just below the line DF receiving no light, and one just 
above it being fully illuminated. This condition is closely 
approximated where the source of light is an open electric 
arc, which gives very sharp shadows. 

346. In the case of a large source, every point of the 
luminous body acts as an independent source. In Fig. 
178, AB represents a candle flame casting a shadow of the 
object CD on the screen EH. Points between F and G 
receive light from no part of the source and are in shadow. 



170 



LIGHT 



The point K receives light from the part of the flame above 
0, but none from the part below it. From F to E and G 
to H the shadow gradually 
fades out, and this part 
shadow is called the pen- 
umbra. When the source 
of light is larger than the 
object casting the shadow, 
the dark shadow, or umbra, 
tapers to a point, while the 
penumbra increases indefi- 
nitely. The shadow of the 
moon cast by the sun tapers 
out (Fig. 179) so that some- 
times the shadow does not 
reach the earth when the moon comes between us and the sun, 
and we have an annular eclipse of the sun. When the earth 




Fig. 178 




Fig. 179. - Condition for annular eclipse of the sun. 

and moon are closer to each other, the shadow reaches the 
earth, and to persons within the shadow the eclipse is total, 
while to those in the penumbra the eclipse is partial. 

347. Rays. When trains of light waves come from 
nearby sources they might be expected to interfere as do 
the ripples in Fig. 143. They do in fact interfere, but the 
spaces concerned are so minute that we do not ordinarily 
observe the effects. It might be supposed that this inter- 
ference would introduce confusion, so that after several 
trains of waves had passed through a common point in 
different directions they would lose something in definiteness, 
but it is not so. Any number of trains of waves may inter- 
sect in the most complex manner, and each train pass on 
beyond the intersection without being tangled in the least. 



PLANE WAVES. PARALLEL RAYS 



171 




Fig. 180 



To trace in a diagram or in imagination the courses followed 
by the light in such a case would be very difficult if we thought 
only of the waves. If, however, we 
draw lines representing the directions 
in which the energy travels from the 
source, the diagrams may be made 
mur^h more simply. These lines, which 
are in general at right angles to the 
wave fronts are called light rays. In 
the diagram the curved lines repre- 
sent wave fronts of light from a point 
source at A, and AB, AC, AD, and 
AE are four of the infinite number of 
rays which radiate from the source. 

348. When light was supposed to 
consist of corpuscles, a ray was 

thought of as a succession of corpuscles moving in a 
straight line. Now we can only define ray as a line 
along which light energy is travelling. Many parallel or 
nearly parallel rays form a beam. Rays which meet at a 
point form a converging pencil or cone. Those which radiate 
from a point form a diverging pencil or cone. 

349. Plane Waves. Parallel Rays. The light waves sent 
out by a luminous point are spherical, like the sound waves 
described in paragraph 286. If we consider a very small 
part of the surface of a very large sphere, it is essentially 
a plane surface. Thus if we consider the light falling upon 
the earth from a star we may say that it consists of plane 
waves. Using the convenient fiction of rays, we may say 
that the rays, w T hich are simply radii of the wave-spheres, 
are parallel. Rays of sunlight are also parallel. That is 
to say, light rays from any point on the surface of the 
sun are parallel rays, though a beam of sunlight shining 
through a small hole is divergent because the sun's disc is 
so large. For most practical purposes, light from a source 
100 meters or more distant from the point of observation 
may be regarded as parallel. 



172 



LIGHT 




Fig. 181 



350. Image Formed by Pin-hole. If a candle be lighted 
in a dark room and placed in a large tight box having a pin- 
hole in one side and a card be 
then held in front of the pin-hole, 
an inverted image of the candle 
will be formed on the card. A ray 
from the tip of the candle flame, 
A, falls at A' on the card. Thus 
a series of points on the card each 
receives a single ray of light from a 
particular point of the flame instead of many rays. The space 
thus illuminated on the card is of the same shape as the flame. 

351. In the same way an image of out-door objects may 
be made in a dark room by means of a hole in the shutter. 
Such an image reproduces faithfully the colors of the ob- 
jects. The image gains in brilliancy and loses in distinctness 
by increasing the size of the hole. In like manner, sun- 
light coming into a room through a small hole of any shape 
forms at a distance from the hole a round spot which is an 
image of the sun. During a partial' eclipse of the sun the 
spots of light on the ground or on a wall where sunlight 
falls through leafy trees are crescent shaped. 

352. Speed of Light. Galileo attempted to determine the 
speed of light by the following method : Two persons were 
stationed at night on hills several miles apart, each having 
a lantern with an apparatus for covering it quickly. One 
observer covered his light. As soon as the other man 
noticed the disappearance of the first light he covered his 
own lantern. The first observer tried to determine the 
time between the covering of his own light and the instant 
when the other disappeared, which should be twice the time 
required for the light to traverse the distance between the 
two stations. No interval was observed. Galileo concluded 
that the speed of light is so great that it takes no appreciable 
time to traverse terrestrial distances. 

353. About 1675 the Danish astronomer Romer made a 
series of very careful observations of the eclipses, occulta- 



EFFECT OF DISTANCE ON ILLUMINATION 



173 




Fig. 182 



tions, and transits of Jupiter's moons. From these observa- 
tions he made tables showing at what instant any one of the 
satellites might be expected to pass into the shadow of the 
planet (eclipse), to disappear behind the planet (occultation), 
or to come between us and the planet (transit). These 
observations were made when the sun, earth, and Jupiter 
were in the relative positions S, E, and J. When the earth 
and Jupiter had moved to the 
positions E' and J' it was found 
that the phenomena occurred more 
than sixteen minutes later than 
had been predicted. When the 
sun and the two planets came 
again into the same relative posi- 
tions as at first, the moons were 
again on time by the schedule 
which Romer had prepared. These 
facts were explained by supposing 
that light takes more than sixteen minutes to cross the orbit 
of the earth. The diameter of the earth's orbit being known, 
the speed of light was obtained by division. Several direct 
methods of measurement have also been devised. A mean 
of the best results is very nearly 300,000 kilometers per 
second. This is often expressed as 3 X 10 10 centimeters per 
second and is equivalent to about 186,400 miles per second. 
Light travels in one second a dis- 
tance equivalent to more than seven 
times the earth's circumference. 

354. Effect of Distance on Illumi- 
nation. If A is a point source and 
BC a square body casting a shadow 
DE on a wall twice as far from A 
as the body BC is, it is clear that 
if BC is parallel to the wall, the 
shadow will also be a square and 

its side will be twice as long as that of BC. The area 
of DE will be four times that of BC, and if BC be removed, 



B . 



D 



^A] 



tr ^ 



Fig. 183 



^y 



174 LIGHT 

the light which fell on it will be distributed over four times 
as much space on the wall (the space which was formerly in 
shadow), and will illuminate it only one-fourth as brightly as 
BC was illuminated. In general, the intensity of illumina- 
tion from a given source is inversely proportional to the 
square of the distance from the source. 

355. Photometry. The law stated in the last paragraph 
enables us to compare the light giving power of various 
sources. Lamps are measured in candle power, the standard 
being a candle of specified material, diameter, etc., giving 
slightly more light than an ordinary paraffin candle. The 
process of comparison is called photometry (light-measure- 
ment). Rumford's method is illustrated in Fig. 184. Lights 
A and B cast on the screen 
MN two shadows of the 
object C. The space DE is 
in shadow from B but is illu- 
minated by A, while FG is 
in shadow from A and is illu- 
minated by B. If one of the ™- 
lights be shifted backward Fig. 184.— Photometry, Rumford's 
or forward until the two method, 
shadows are of equal inten- 
sity, we conclude that the lights are illuminating the screen 
equally. Suppose that the shadows are equal when A is two 
meters from the screen and B one meter. If A produces at 
two meters' distance the same illumination that B produces 
at one meter it must be four times as bright as B, for an 
object one meter from A would be four times as brightly 
illuminated as the space DE, and therefore four times as 
brightly as it would be by B at the same distance. In 
general, divide the smaller distance into the larger and 
square the quotient ; the result is the ratio of the lights. 

356. Bunsen's method is shown in diagram in Fig. 185. 
C is a paper screen with a grease-spot in the middle. If a 
light be placed at A, an observer at F sees the grease-spot 
darker than the rest of the screen, because, since the greased 




DIFFUSED REFLECTION 175 

paper transmits more light than the other part, it reflects 

less and therefore looks darker. If now A be extinguished 

and another light placed at B, the observer at F sees the 

grease-spot lighter than the q 

surrounding paper because it £ " J$ 

transmits more light. When *""" ' 

both lights are shining the „ ioe ™ . ^ , 

fe . . . . . Fig. 185. — Photometry, Bunsen's 

screen may be placed in such method 

a position "that the grease-spot 

is neither lighter nor darker than the surrounding paper. 

The illumination is now equal on the two sides, and as before 

the square of the ratio of the distances gives the ratio of the 

intensities of the lights. 



REFLECTION OF LIGHT. 

357. Law of Reflection. Suppose light coming in the direc- 
tion AO to strike the smooth surface MN, and let CO be 
a perpendicular to the surface. AO is called an incident ray, 
CO the normal to the surface at 0, and ~, ~ 
the angle AOC the angle of incidence \^ i ^ 
of the ray AO. The light will be re- a#-^^N^ fo/* xr 

fleeted in the direction OB, making ^ 2*£< dX. 

the angle of reflection, COB, equal to 

AOC. One of the earliest laws of optics to be discovered 
was the Law of Reflection; the angle of reflection is equal to 
the angle of incidence. This is true whether the surface be 
plane or curved. 

358. Diffused Reflection. We 
see non-luminous objects by 
means of the light which they 
reflect to the eye. If the surface 
is rough, light from one or many 
sources falling on the object is FlG . 187.— Diffused reflection, 
reflected in many directions, and 

this reflected light entering our eye gives us a picture of the 
object. Any part of the object is seen in the direction from 




176 



LIGHT 




Fig. 188. 



i4..-,--4 



Visual angle. 



which the diffused light from it enters the eye. The dia- 
gram (Fig. 187) illustrates how parallel light is diffused by 
a rough surface. 

359. Visual Angle. An eye 
at E sees the object AB, whose 
apparent size depends on the 
difference of direction of the 
rays AE and BE from the ex- 
tremities of the object. This 
difference of direction, the angle 

AEB, is called the visual angle. If the same object is 
placed farther away, as at A'B' ', the visual angle is made 
smaller and the object appears smaller. 

360. Plane Murors. A smooth surface reflects light waves 
which fall upon it without breaking them up. If such a 
surface is flat it forms a plane mirror. Let AB be a mirror 
surface, CD an object in front of it and E the point of 
observation. A ray of light 

from C, striking the mirror ^\.\ r *'.''™ 

at F is reflected to the eye, 
and appears to come from 
C, since we see a thing in 
the direction from which the 
light sent by it enters our eye. 
In like manner a ray from D 
seems to come from D' ', and the observer seems to see the 
object at CD'. Suppose DC to be a line of print so placed 
that to an eye at G it would read from D to C. The eye 
at E will see an image that reads from D' to C, that is 
backward. This effect of a mirror is called lateral inversion 
or mirror inversion. 

361. The image made by a plane mirror is of the same 
size as the object appears. The visual angle C'ED' is equal 
to CE f D, so that the image appears of the same size that 
the object would to an eye at E' (with the mirror removed). 
CD' is a virtual image. There is really nothing behind the 
mirror. CD appears to be at CD' simply because the light 




Fig. 189. — Image by plane mirror. 



MULTIPLE REFLECTIONS 177 

from it has been reflected by the mirror, and so enters the 
eye from a changed direction. 

362. Definition of Mirror Surface. In order to reflect un- 
broken light waves, a surface must not only be smooth 
to the touch but so smooth that the irregularities are small 
compared with the wave-lengths of light. A piece of close- 
grained wood may be made so smooth that we cannot see 
or feel any irregularities in the surface, but it will not serve 
for a mirror. The microscope shows holes in the closest- 
grained wood, and the irregularities being large compared 
with the wave-lengths of light, they break up the waves. 
Each tiny roughness on the surface thus acts as a centre 
of disturbance, and sends out a new train of waves. Thus 
the body which diffuses light acts in some sense like a source, 
and we may now see why it is that we see non-luminous 
bodies by means of the diffused light which they reflect. 
A polished surface of metal or glass has no pores which can 
be seen by any known device, and such a surface acts as a 
mirror. A perfect plane mirror would be itself invisible, 
since it would reflect unbroken trains of waves, and show 
only reflected objects. We see mirrors because of dust or 
other imperfections on the surface. The best mirrors are 
made of silver, which reflects a very large part of the light 
which falls upon it, transmitting none and absorbing very 
little. Silver, however, is easily tarnished, and is expensive. 
For most purposes, therefore, mirrors are made by depositing 
a very thin film of silver on glass, protecting it by a coat of 
paint, and then looking at it through the glass, which 
protects it from injury. If we hold a candle flame in front 
of a mirror, two images may be seen; one from the silver 
surface and one from the glass. 

363. Multiple Reflections. By means of two or more 
mirrors many images of the same object may be seen at the 
same time. One instance is shown in Fig. 190. M, M', 
are parallel mirrors, face to face; L is a bright point between 
them, and E the point of observation. A ray from L re- 
flected at gives an image of L, appearing to be at U, 

12 



178 



LIGHT 



Another ray, reflected at S and again at S' gives a second 
image L" . A ray striking at R, reflected again at R f and 
again at R" gives a third image U-". Twenty or more images 
of a candle flame may thus be seen. U and U" are laterally 



& 




M' X' 



IT 



Fig. 190. — Multiple images, parallel mirrors. 



inverted, L" having been twice reflected, is not, and so they 
alternate down the line. It is convenient to locate L" 
and U" by regarding them as images which the mirror M' 
forms of the images formed by the mirror M. Thus L" 
is an image of L' v , the two being at equal distances from M'. 
364. Concave Spherical Mirrors. Parallel light falling on 
a plane mirror remains parallel after reflection, but if the 
mirror surface is curved, the reflected light will not be parallel. 
Let AB represent a mirror which is a part of a concave 
spherical surface, whose centre is 
at C, and let DA and EB be 
parallel rays of light falling upon 
it. CA and CB are perpendic- 
ulars, or normals, to the surface 
at A and B. The ray DA is re- 
flected in the direction A H so as 
to make the angle CA H equal to 
DA C. In like manner EB is re- 
flected in the direction BG. If the mirror includes a very 
small fraction of the spherical surface, all parallel rays 
falling upon it will, after reflection, pass through the same 
point. This point F, called the principal focus of the mirror, 
is half way between C, the centre of curvature, and the 
surface of the mirror. 




Fig. 191. — Concave mirror. 



REAL IMAGE BY CONCAVE MIRROR 



179 




Fig. 192. — Conjugate foci of concave 



365. Conjugate Foci of Concave Minor. Parallel rays, 
that is, rays from an infinitely distant source, are brought 
to a point at the principal focus F, but if a divergent cone of 
rays from a source /fall on the concave mirror AB, they will 
be brought to a focus at /'. 

This point is farther from AA: £L 

the mirror than F, for 

since the angle fAC is less 

than DAC, CAf will be 

less than CAF. If / is 

brought closer to the mirror, 

/' will manifestly be farther 

away, and there will thus be 

an infinitely large number 

of pairs of points so related that light issuing from one of 

them will be brought to a focus at the other. Such a pair of 

points are conjugate foci. If the source of light is at /', the 

rays which strike the mirror are brought to a focus at /. If 

the source is at F, the mirror sends out the reflected rays in a 

parallel beam. The line fM passing through the centre of 

curvature is an axis of the mirror. Any line through C is an 

axis, and rays coming from a point on any axis are brought 

to a conjugate focus on the same axis, while rays parallel 

to any axis are brought to a principal focus on the same axis. 

366. Real Image by Concave Mirror. Suppose AB to be 
an illuminated object placed in front of a concave spherical 
mirror DK. Three rays from 
A to the mirror are traced in 
the diagram. The ray ACK, 
following a radius of the 
spherical surface, strikes at 
right angles and comes back 
along the same line. AE, 
parallel to the axis LG, passes 
through the principal focus 

F, and A D is so reflected as to make the angle BDA' equal 
to ADB. All other rays from A which strike the mirror also 




Fig. 193. — Real image by concave 



180 LIGHT 

come to a focus at A', which is a focus conjugate to A, and 
lies on the axis AK. In like manner all the rays from B 
which strike the mirror will be brought to a focus at B', and 
rays from each point of the object will be brought to a focus 
at a corresponding point. If a card be placed at A'B' ', an 
inverted image of the object will be formed upon it. That 
is to say, the light from AB reflected from the mirror and 
falling on the card will make an actual illuminated picture 
of AB at A'B'. 

Such a picture is ealled a real image. It may be seen by 
a number of persons at once, and has the same appearance 
to all of them. It has an existence entirely apart from the 
eye of the observer, and one can point to its parts as to the 
parts of a printed picture. A virtual image, on the contrary, 
has no existence apart from the eye of the observer. We 
seem to see things where there is nothing. No two persons 
can see the same virtual image, because the appearance is 
not the same from any two points of view. 

367. Size of Real Image. In Fig. 193 the object is farther 
from the mirror than the centre of curvature, and the 
image nearer. The object may equally well be in the 
nearer position and the image in the farther one. The 
dimensions of image and object are proportional to their 
distances from the centre of curvature. It is evident 
from the similar triangles ABC and A'B'C that AB will be 
twice as long as A'B' if the line AC is twice A'C. It may 
also be shown that the dimensions of image and object are 
directly proportional to their distances from the mirror. 
If a small flame be placed close to the centre of curvature, an 
inverted image of the same size as the flame may be obtained 
on a card held at one side of the flame, and if the flame be 
placed between the principal focus and the centre of curvature 
an inverted larger image will be formed beyond the centre 
of curvature. 

368. Virtual Image by Concave Mirror. As the flame is 
placed nearer and nearer, the image is formed farther and 
farther away, and finally when the flame is at the principal 



CYLINDRICAL MIRRORS 



181 



focus, the reflected rays are sent out parallel, and no real 
image is formed. A real image is formed by a mirror (or 
lens) only when rays of light from each point of an object 
are brought to a focus at a corresponding point of the image, 
and of course parallel rays do not come to a focus. If the 
flame is placed closer to the mirror than the principal focus, 
an eye looking at the mirror sees an erect, laterally inverted, 





Fig. 194 



Fig. 195. — Virtual image by concave 
mirror. 



virtual image, just as in a plane mirror, except that here 
the image is larger than the object. Fig. 194 shows how 
rays from a point of the flame are sent out divergent. Fig. 
195 shows why the virtual image is larger than the flame. 
The rays AO and BD on being reflected from the curved 
surface to the eye at E are rendered so convergent by re- 
flection from the curved surface as to render the angle of 
vision A'EB' larger even than A EB. 

Convex Spherical Mirrors can- 
not make real images because 
they do not tend to make 
rays converge to a focus, but 
to make them diverge. They 
form virtual, erect images, 
smaller than the object. The 
explanation of the smaller size 

is exactly analogous to that just given for the opposite case. 
In the figure the image appears much smaller than the object. 

369. Cylindrical Mirrors. A convex cylindrical mirror 
gives distorted virtual images. The dimension of a body 
which is parallel to the axis of the cylinder is shown of normal 




Fig. 



196. — Virtual image 
convex mirror. 



by 



182 LIGHT 

size in the image, since the mirror has no curvature in that 
direction, while dimensions perpendicular to the axis are 
shown on a reduced scale because of the curvature of the 
surface. A concave cylindrical mirror shows normal dimen- 
sions parallel to the axis and magnified ones perpendicular 
to it. Mirrors having different curvatures in different 
directions and in different parts often give very grotesque 
effects. 

370. Caustic of Reflection. Parallel rays falling upon a 
curved surface of large area are brought to a single focus 
only when the surface of the 
mirror is of such shape that 
the cross-section is a para- 
bola. If the surface be spher- 
ical or cylindrical the rays are 
reflected in such a manner as 
to form the curious curve 
called the caustic of reflection. 
The diagram shows the man- 
ner in which the curve is FlG 197 .Z Callstic of Reflection, 
formed. Caustics are often 

seen in teacups or in glasses, or on the table within a silver 
napkin ring. 

EXERCISES AND PROBLEMS. 

1. An incandescent lamp 2.5 meters from a wall, and a 
candle .6 of a meter from it, ^ive shadows of a stick side by 
side on the wall, of equal intensity. How many times as 
much light as the candle does the lamp give? 

2. The nearest fixed star, Alpha Centauri, is about 
30,000,000,000,000 kilometers from the earth. How long 
does light take to come from it to us? 

3. Two mirrors are at right angles to each other, and a 
candle flame is in the angle thus formed. How many 
images of the flame can be seen? Make a diagram. 

4. A concave spherical mirror has a radius of curvature 
of 8 inches. Make a diagram showing the formation of an 




REFRACTION 



183 



image of an arrow l\ inches long, 12 inches from the mirror, 
at right angles to the principal axis. 

5. Why is the image seen in one side of the bowl of a spoon 
inverted and the other not ? 




REFRACTION. 

371. Refraction of water waves has been briefly explained 
in paragraph 269. Light waves behave in much the same 
manner. The speed of light is affected by the medium 
through which it passes, and in passing obliquely from one 
medium to another, the direction is changed in consequence 
of the change of speed. The dia- 
gram represents a beam of light 
passing through air and striking 
the water surface M N. A is a 
wave-front just striking the water 
at 0. BCD is the same wave-front 
when it has moved through the 
space A B in air. The part in the 
water has moved more slowly, and 
has reached the position CD. 
When the wave-front has all en- 
tered the water it has the position EF, and since the 
direction is at right angles to the wave-front, the beam 
now has the new direction EG, more nearly perpen- 
dicular to the surface of the water than before. This 
change of direction is well ™ 
illustrated by the behavior 
of a sled, one runner of 
which strikes a patch of 
ground bare of snow. 

372. Place a coin or 
bright button in the bottom 
of a basin, as at C. Fix a 
card with a hole in it at E so that an eye looking through the 
hole just cannot see the coin. Without disturbing the coin, 



Fig. 198 




Fig. 199 



184 LIGHT 

fill the basin with water. The coin is now visible; the light 
from it follows the course COE, and it appears to be at C '. 

373. Optical Density. In general, the speed of light is 
less in denser media than in rarer ones, so that the terms 
denser and rarer came to be used in describing the resistance 
which media offer to the passage of light waves. The optical 
densities of two media are proportional to the speed of 
light in them, and have no definite relation to their volume 
densities. For instance, water is a fourth denser than alco- 
hol, but the speed of light through it is 2 per cent, greater 
than through alcohol. 

374. Index of Refraction. When light passes obliquely 
from one medium to another of different density, its direc- 
tion is changed, and if there is a definite surface between 
the two media, as between air and water, some of the light 
will be reflected at the surface and the rest will pass on into 
the second medium. The ratio of the . 

speed in the first medium to the speed in the X l (j 

second is called the Index of Refraction. 1 \ i 

In the figure, AOB represents a ray pass- \ \V* / 

ing from air to water, OC being the per- V ^jr~ 7 

pendicular to the surface. AOC is then \ _I\d / 
the angle of incidence, and DOB the \___L__/ 
angle of refraction. If the light be Fig. 200 

passed from water to air DOB is the angle 
of incidence and AOC the angle of refraction. The angle 
is always greater in the medium of less optical density. 

375. Total Reflection. Critical Angle. When a beam of 
light passes perpendicularly from one medium to another 
of different density, that is, when the angle of incidence is 
0°, its speed is changed, but not its direction. As the angle 
of incidence increases, the change of direction is increased. 
If the beam is passing from a rarer medium to a much denser 
one, the amount of refraction becomes very large as the 

1 The index of refraction may also be defined as the ratio of the sine 
of the angle of incidence to the sine of the angle of refraction. 



TOTAL REFLECTION. CRITICAL ANGLE 



185 




Fig. 201 



angle of incidence approaches 90°. The diagram shows 
the actual direction taken by light passing from air to glass 
at an angle of 80°. The index of refraction from air to 
glass is about J-, so the 

distance AO must be • 

lj times CB, since the 
light travels the distance 
AO in air in the same 
time that it travels from 
C to B in the glass, and 
distances traversed in 
equal times are propor- 
tional to the speeds in 
the two media. Light striking a glass surface at such an 
angle is nearly all reflected, as shown by the dotted lines, 
but a small part enters the glass, taking the direction CD. 
It is clear that no further increase in the angle of incidence 
can greatly increase the angle of refraction EOF, that is to 
say, the angle of refraction is approaching a maximum value. 
376. Now let us consider what happens when light passes 
from glass to air, the angles being the same as in Fig. 201. 
The index of refraction is now f . A large part of the light 
is reflected back into the glass, but a part escapes, taking 
the direction OG. The 
limits of the reflected beam 
are shown by the dotted 
lines CA and OB. The 
angle of incidence DCE 
is about 40°, and if it be 
increased to 42°, no light 
will escape, but all will be 
reflected back into the 

glass. This phenomenon is called total internal reflection, 
and the smallest angle at which it takes place is called the 
critical angle. It will be observed that total reflection only 
occurs when light is attempting, so to speak, to pass from 
a denser to a rarer medium. 




186 



LIGHT 



377. The silvery appearance of an empty test-tube 
thrust into a glass of water is due to total reflection at the 
surface between glass and air. A silver spoon in a glass of 
water may be seen totally reflected by looking up at it 
through the side of the glass. 

378. Refraction by the At- 

mosphere. Let R be a ray ^ \ -R 

of light from a star entering 
the earth's atmosphere. As 
it penetrates more deeply it 
meets layers of increasing 
density and is refracted more 
and more, thus describing a Fl<3 ' 203.-Atmo S pheric refraction. 

curved path. An observer at A sees the star in the direc- 
tion AR'. The displacement thus caused amounts to about 
one-half a degree for objects near the horizon. 

379. Mirage. The sand of deserts becomes so hot some- 
times that a layer of air next to the ground becomes hotter 
than that above it. A ray from T follows a curved path and 





-^<fjT' 



Fig. 204. — Desert mirage. 



is totally reflected at A. Thus to an eye at E the tree appears 
inverted at T', as well as in its normal position at T, along 
the line ET. 



REFRACTION THROUGH A PRISM 187 

Table Showing Indices of Refraction from Air to Various Substances, for 
Sodium Light, at 20° C; also the Critical Angles. 

Substance. Index. Critical angle. 

Water 1.334 48° 33' 

Crown glass 1.52± 41° 8' 

Flint glass 1.63± 37° 50' 

Carbon disulphide . -. . . 1.628 37° 54' 

Alcohol 1.361 47° 17' 

Turpentine 1 . 472 42° 47' 

Quartz (ordinary ray) . . . 1.544 40° 22' 

Iceland spar (ordinary ray) . 1 . 658 37° 6' 

Rock salt 1.544 40° 22' 

Canada balsam 1 . 528 40° 53' 

Diamond 2.470 23° 53' 

380. Refraction through a Prism. A beam of light passing 
through a piece of glass with parallel sides leaves the glass 




RE 




Fig. 205 



Fig. 206 



in a direction parallel to that in which it entered, since the 
edge of the beam which lagged behind in entering gets out 
first and catches up, as may be seen in Fig. 205. A line of 
print seen obliquely through a strip 
of thick glass has the appearance 
shown in Fig. 206, due to the dis- 
placement of the light in passing 
through the glass. If, however, the 
sides of the glass are not parallel, we 
have what is commonly called a glass 
prism, and the direction of the beam 
after passing through will not be the same as before. In 
the case shown in Fig. 207 the side of the beam which 







Fig. 207 



188 



LIGHT 




entered the glass last escapes before the other, and so 
the beam is bent in both cases in the same direction. 

381. Lenses. A piece of 
glass or other transparent 
material having one or both 
of its opposite surfaces 
spherical or nearly spherical 
is called a lens. The dia- 
gram shows the cross-sections 
of some forms of lenses. E 
is essentially a convex lens 

because it is thicker in the middle, and F essentially con- 
cave because it is thinner in the middle. 

382. Converging Lenses. A convex lens is sometimes 
called a converging lens. The reason for this is shown in 
Fig. 209. The line CD, passing through the middle of the 
lens, perpendicular to the plane of its edge, is the principal 
axis of the lens. A ray of light parallel to the principal axis 
striking the lens at A is deflected toward the axis, as 



A, double convex; C, double concave; 
B, plano-convex; D, plano-concave. 

Fig. 208.— Lenses. 





Fig. 209 



Fig. 210 



explained in paragraph 380. In the same manner a ray 
striking at B is deflected toward the axis. All parallel 
rays which fall upon a properly shaped convex lens are 
brought to the same point, called the principal focus. This 
point is nearer to a more convex lens than to one which 
is less convex. The position of the principal focus also 
depends on the refractive index of the glass. 

Concave lenses are diverging lenses, since parallel rays 
falling upon them are rendered divergent (Fig. 210). 

383. Conjugate Foci of a Convex Lens. As in the case of 
a concave spherical mirror, a convex lens had an indefinite 



THE CONJUGATE FOCAL DISTANCES 



189 




Fig. 211. 



-Conjugate foci of con. 
vex lens. 



number of pairs of conjugate foci, light issuing from a point 

source farther from the lens than the principal focus being 

brought to a conjugate focus 

on the other side of the lens 

(Fig. 211). As the source of 

light is brought nearer to the 

lens, the other conjugate focus 

recedes, as in the case of the 

concave mirror. 

384. Real Image by Convex Lens. If a convex lens be 
placed in direct sunlight and a piece of paper held behind it, 
the light coming through the lens may be concentrated into 
a spot much smaller than the lens. By varying the relative 
positions of lens and paper, a point may be found where the 
spot of light is smallest. This point is the principal focus, 
and the spot is an image of the sun, light from each part 
of the sun's disc being brought to a focus at a corresponding 
point of the image. If the lens is very convex, the image 
will be small and close to the lens, and if the diameter of 
the lens be two inches or more, so much energy may be 
concentrated in a small space as to set fire to the piece of 
paper on which the image is formed. 

385. A convex lens may be so placed as to form a real, 
inverted image of any source of light or illuminated object, 
the object being at one 
conjugate focus and the 
image at a corresponding 
one, as in the case of a 
concave mirror. Rays 
from A (Fig. 212) which 
pass through the lens are brought to a focus at A' , and since 
rays from every point of the object AB are brought to a 
focus at a corresponding point, the image A'B' is formed. 

386. The Conjugate Focal Distances are connected with the 




Fig. 212. — Real image by convex lens. 



principal focal distance by the equation — |- 
a and b are the distances from the lens 



7 = ,, where 

f 

)f a pair of 



190 



LIGHT 



conjugate foci, and / is the principal focal distance. 1 This 
formula affords a convenient means of determining the 
principal focal distance of a lens, since a and b may be 
measured and / calculated. 

387. Convex Lens a Magnifying Glass. Not only does the 
convex lens behave like the concave mirror in forming real, 
inverted images, it also resembles it in giving virtual, 
erect enlarged images. Fig. 214 2 shows the cause of the 

1 Demonstration : — Let C be the centre of the lens EG, and DD' its 
principal axis. Suppose the object AB placed so that a point of it 
is on the principal axis at D, the object being at right angles to the 
principal axis and the distance AD equal to the radius of the lens. 
The ray AC A' passing through C is assumed to travel in a straight 




line, which is not strictly true, since it is bent both on entering and 
leaving the lens. The ray AE, passing through the edge of the lens, 
being parallel to the principal axis, is refracted through the prin- 
cipal focus, F. Now from the similar triangles ACD, and A' CD', 



AD 



PSL, and from the similar triangles, EFC, and A'D'F, 
D'C 



But CE 
DC 



AD, therefore since the first members are 



A'D' 

CE CF 
A'D' D'F 

equal, = -^. Now CF is the principal focal distance, and DC 

D'F D'C 

and D'C are a pair of conjugate focal distances. Let DC = a, D'C = b, 

and CF = /. Then D'F is b — / and we have —I— = % Clearing of 

i b — f b 

fractions, bf = ab — af. Transposing af, bf + af = ab. Dividing 
through by a + b, f 



-°L b - or dividing by dbf,± + I 
a + b a o 



2 The image usually appears a little farther away than the actual 
distance of the object, when we use a small magnifying glass; a fact 
which is not very easy to explain. 



THE PROJECTING LANTERN 



191 



magnification. To an eye at E the object A B if there 
were no lens would subtend the angle AEB. When the 
lens is placed between the eye and the object, a ray AC 
is refracted so as to enter the eye in such a direction as to 
appear to come from A', and a ray from B appears to come 
from B f , so that' the visual angle is increased from AEB 
to A'EB' ', and the object therefore looks larger than before. 
In order to be magnified in this manner, the object must 
in general be closer to the lens than the principal focal 
distance. 



m 



B^ 




^>E 



Fig. 214 




388. Images by Concave Lenses are always virtual, erect, 
and smaller than the object. In Fig. 215 the lens causes 
the object AB to subtend the smaller angle A'EB' . 



OPTICAL INSTRUMENTS. 

389. The Camera, used chiefly for making photographs, 
is shown in diagram in Fig. 216. It consists of a light- 
tight box B of adjustable length, having a lens at L and a 
ground-glass screen or window 
S. The length of the box is 
so adjusted as to secure on S 
a sharply defined picture of 
the object to be photographed. 
A sensitive plate is then substituted for the ground glass, 
exposed for a short time to the action of the light, and after- 
ward subjected to chemical processes which develop and fix 
the picture upon it. 

390. The Projecting Lantern is shown in Fig. 217. In its 
ordinary form it is used to throw an enlarged image of 




Fig. 216. — Camera. 



192 LIGHT 

a transparent picture on a wall or screen. The picture, 

called a " lantern slide," is placed at S in front of a large 

pair of lenses C, called condensers, near whose principal 

focus is a strong light L. In front 

of the slide is placed the project- r-V- 

ing lens P, whose distance can be | \ 

so adjusted as to throw a sharply ' \- J ~jf 

defined image on the screen. The r/i 01 « x» ■ *• i * 

, to . . . . . Fig. 217. — Projecting lantern, 

best results are obtained, as is 

also the case with the camera, by using a pair of achromatic 1 
lenses at P, sometimes called a compound lens. By a modi- 
fication of the projecting lantern, images of opaque objects 
may also be obtained. 

391. The Eye is a camera in which the network of nerves 
at the back of the eyeball, called the retina, takes the place 
of the sensitive plate. Light from A, entering the curved 
surface of the cornea C and passing through the aqueous 
humor and the crystalline lens L is brought to a focus at 
A' on the retina, and an 

inverted image of the ''** ^^ / j^ \ jf 

object is thus formed. 2 
While the eye is observ- 
ing the object AB, a more FlG 218 __ Norma i ^T 
distant object could not 
be seen clearly, the light from it being brought to a focus 
before reaching the retina. To enable us to see distinctly 
objects at different distances, the shape of the lens is changed 
by means of the ciliary muscles. Hold up a finger between 
your eye and some object across the room. Close one 
eye. Look at the finger and then at the distant object. 

1 See paragraph 420. 

2 The question is often raised, "Why do not objects appear upside 
down, since the image on the retina is inverted?" Look at a tree, and 
slowly turn the head over until the line joining the eyes is vertical. 
The tree does not appear to turn over and lie down. The apparent 
positions of things do not depend on the positions of their images on 
the retina. 




ASTIGMATISM 193 

Movement in the eye can be distinctly felt. An impression 
once made on the retina does not immediately fade. A 
spark on the end of a stick which is being whirled rapidly 
around may thus appear as a circle of fire. This fact is 
expressed in the phrase "persistence of vision." 

392. Far-sightedness. The power to change the shape 
of the crystalline lens is called the power of accommoda- 
tion. With advancing age this power is partly lost, so that 
most persons over forty-five years old cannot see clearly 
objects at a distance of 30 cm. (12 inches) or less without 
an effort which soon becomes tiresome. Such persons 
are said to be far-sighted, because they cannot see near 
objects clearly. They use glasses whose lenses are convex, 
and the converging power of the glasses being added to that 
of the aqueous humor and crystalline lens, a clear image 
is obtained on the retina when the object is at a convenient 
distance from the eye. Sometimes young persons are far- 
sighted, the crystalline lens being insufficiently convex. 

393. Near-sightedness. On the other hand, persons whose 
crystalline lenses are too convex can see objects clearly 
only when they are held very close to the eye. Such 
persons are near-sighted. An 
object at a distance cannot 
be seen distinctly because, the 
focal length of the lens being 

too short, the rays are brought "^ 2 19.-Near-sighted^. 
to a focus before they reach 
the retina. The defect is corrected by concave glasses. A 
person with normal eyes can picture to himself the plight 
of the near-sighted person by holding a convex lens near 
his eye and then noting how close he must hold print in order 
to be able to read it. 

394. Astigmatism. In a perfect eye the curvature of the 
cornea is equal in all directions. When this is not the case, 
the images on the retina are likely to be distorted, somewhat 
in the manner of those seen reflected from the bowl of a 
spoon. This defect, called astigmatism, is remedied by using 

13 




194 



LIGHT 



a cylindrical lens of the proper curvature placed in the right 
position. If such a lens falls out and is wrongly replaced it is 
much worse than none. Nearly all eyes have some astigmatism. 

395. The Compound Microscope, the 
plan of which is shown in Fig. 220, is 
employed instead of the simple mag- 
nifying glass in looking at very small 
things or parts of things. The object, 
which is shown at AB, must be strongly 
illuminated. is a lens of short focus 
called the objective, which forms a real 
image at A'B' ' . Another convex lens, E, 
the eye-piece, magnifies this image, form- 
ing the virtual image A"B" . Objects 
smaller than a half wave-length of yellow 
light cannot be distinctly seen with the 
microscope. This limit is reached at a 
magnifying power of about 2500 " diam- 
eters." That is, the object is made to 
appear to occupy an angle 2500 times as 
large as it would really subtend at a 
distance of 25 or 30 cm. from the eye 
(the distance of distinct vision). 

396. The Telescope. Most things can 
be seen with sufficient distinctness by 
coming close to them, and thus increasing the visual angle. 
If the object is very small, we cannot see it well even at 
the shortest distance at which distinct vision is possible, 
and must use a microscope. ^ 
But sometimes we wish to see 
things which we cannot con- 
veniently approach, and the 
instrument employed in this 
case is the telescope. It has, 

like the microscope, an objective and an eye-piece, and 
they serve the same purposes as in the microscope. The 
objective makes an inverted real image of the distant 




O 
A B 

Fig. 220. — Compound 
microscope. 



? 



Fig. 221. — Refracting telescope. 



FIELD GLASS 195 

object, and the eye-piece magnifies this image. In the 
case of the microscope the objective lens is placed near 
the object and a large real image is formed far from 
the lens. In the telescope, since the objective cannot be 
placed near the object, a large image is formed by making 
the objective of long focus. Of course the image is not 
larger than the object, but the farther it is from the objective 
the larger it is. A main purpose in making the objective 
of the telescope large in diameter is to enable it to gather 
much light and so form a bright image. The eye-piece is 
similar in telescope and microscope, commonly a compound 
lens. The shorter the focus of the eye-piece the greater 
will be the magnifying power in both cases, but it will be 
observed that an objective of long focus is necessary for high 
magnifying power in the telescope, and one of short focus in 
the microscope. 

397. Magnifying Power of a Telescope is measured in "di- 
ameters." Thus a telescope magnifies six diameters when 
it causes an object subtending a visual angle of one-tenth of 
a degree to occupy six- tenths of a degree. The magnifying 
power is the ratio of the principal focal length of the objective 
to that of the eye-piece. 

398. Field Glass. A single long focus lens may be used as 
a telescope, since it will make a real inverted image which 
fills a larger visual angle than the object (Fig. 222). The 



Fig. 222 — Single lens as a telescope. 

lines AE and BE show the angle which the object AB would 
subtend. The lens L makes an image A'B' which subtends 
a larger angle. Only a very small part of an object can be 
seen at once in this manner. 

By using an objective of comparatively short focus and 
for an eye-piece a concave lens placed within the principal 
focal distance, the very convenient form of telescope called 



196 



LIGHT 



the field glass or opera glass is made. The first astronomical 
telescope, made by Galileo in 1609, was of this type. The 
diagram illustrates the principle of the instrument. MN 
is the objective, E the eye-piece. The solid lines passing 
through the edges of the objective and converging toward 
B represent rays from the top of a distant object, the broken 
lines converging toward A, rays coming from the bottom. 
If the eye-piece were removed the rays would focus at A B, 




Fig. 223. — Galilean telescope. 

forming an inverted image. The concave eye-piece renders 
the convergent rays slightly divergent, so that to an eye 
behind the eye- piece they appear to be coming from sources 
at A' and B' ', thus giving an erect apparent image of the 
object. Two such instruments are arranged so that the 
observer sees through one with one eye and the other with 
the other, thus giving the advantage 
of binocular vision (paragraph 401). 
399. Another form of field glass, 
recently invented, is a pair of ordi- 
nary telescopes shortened by insert- 
ing two pairs of totally reflecting 
prisms, thus causing the light to 
traverse the length of the instru- 
ment three times. The objectives 
are at 0, the prisms at P, and the 
eye-pieces at E. One advantage 
of this instrument is its wide field of view, and another is 
that the increased distance between its two objectives 
increases the stereoscopic effect (paragraph 403). 




Fig. 224. — Zeiss field glass. 



BINOCULAR VISION 



197 




400. Reflecting Telescope. Sir Isaac Newton invented the 
form of telescope shown in Fig. 225, in which a concave 
mirror takes the place of 

the lens as an objective. 
The reflected rays are caught 
on the mirror M and again 
reflected into the eye-piece E. 

401. Binocular Vision. No 
single picture of an object 

can have quite the same appearance as the object itself, 
because the picture is flat, while in looking at the object 
we are able to tell which parts are nearer and which are 
farther away. We can do this because we have two eyes, 
which give us slightly different pictures of things, and our 
impression is made up by the combination of these two 



Fig. 225. — Newtonian reflector. 





Fig. 226 



pictures. If we look at a cube 2 cm. in size at a distance of 
30 cm., we may get such a picture as A with the left eye, and 
at the same time a picture like B with the right. When 
we look with both eyes we get these pictures superimposed, 
and so receive the impression of the solidity of the cube. 
It does not look flat. 

402. If two photographs of the same object be taken from 
stations a few inches apart and mounted side by side, and 
we then look at one with one eye and the other with the other, 
we may get the same effect that the object itself gives. 
This is somewhat difficult, however, for we must look at 
them " cross-eyed ,, in order ,to see them superposed. By 



LIGHT 



looking in this manner at the pictures of the cube (Fig. 
226), they give the impression of a solid. This is best done 
by putting a cardboard partition between the pictures, so 
that the right eye can see B only and the left A only. 

403. The Stereoscope superposes the picture for us. The 
diagram shows the plan of the instrument. Two prisms, 
P and P f are mounted with their centres about as far apart 
as our eyes, with a partition D between. A point at A in 
the right-hand picture is seen at B by the right eye in conse- 





Fig. 227. — Plan of stereoscope. 



Fig. 228 



quence of the refraction of the light by the prism P, while 
the corresponding point A' of the other picture appears 
to the left eye L to be also at B, and so the pictures are super- 
posed. In practice the prisms are pieces of a convex lens, 
cut as shown in Fig. 228 and placed edge to edge. They 
thus magnify the pictures slightly. 



EXERCISES AND PROBLEMS. 

1. A pair of conjugate focal distances for a certain convex 
lens were 21 cm. and 51.25 cm. Find its principal focal 
distance. 

2. Draw a diagram showing the passage of a parallel 
beam of light 4 cm. wide from air to water at an incident 
angle of 45 degrees. 



DISPERSION. THE SPECTRUM 



199 



3. Why do objects seen through window panes often appear 
distorted ? 

4. A distant object is photographed with a lens whose 
principal focal distance is 20 cm. At what distance must 
one look at the picture that it may have the same apparent 
size as the object (viewed from the point from which the 
picture was taken) ? 

5. Can a convex lens whose curvature is not equal in all 
directions form a sharply denned real image? 

6. Can the lens of exercise 5 give a clear virtual image ? 

7. The Lick telescope, Mount Hamilton, California, has 
an objective whose principal focal length is 57 feet. With 
an eye-piece whose principal focal length is one inch, what 
will be the magnifying power? 

8. Why can better astronomical observations be made 
on objects directly overhead than on those near the horizon? 

9. What is the speed of light in water? In diamond? 
(See Table of Indices of Refraction.) 



COLOR. 

404. Dispersion. The Spectrum. If a triangular glass 
prism be placed in a beam of sunlight, not only is the course 
of the beam changed by refraction (paragraph 380), but the 
white light is separated, or 
dispersed, forming a band of 
colors, called the spectrum. 
This beautiful experiment is 
due to Sir Isaac Newton. He 
distinguished seven colors 
in the spectrum: violet, 
indigo, blue, green, yellow, 
orange, and red, violet being 
refracted most and red least. 
We might give more than seven names to the colors, since 
they shade into each other, or we might reduce the number 
to four: red, yellow, green, and blue. 




Fig. 229. — Spectrum by prism. 
(The distance from prism to screen 
should be several hundred times the 
width of the prism.) 



200 LIGHT 

If at a suitable distance from the prism the spectrum 
be received upon a large lens, the light may be collected into 
a white image of the hole through which the beam is entering. 
This shows that after white light has been split up into colors 
those colors may be recombined and give white. 

405. Cause of Difference of Color. White light is made up 
of infinitely complex waves. The range of frequencies 
represented is very large. A violin string vibrating so as to 
give a very large number of overtones gives a very faint 
picture of the condition of the ether when its vibrations, 
give us the impression of white light. Of the visible spectrum 
produced by the separation of these various rates of vibra- 
tion, violet has the highest frequency and red the lowest. 
The vibration frequencies are represented by numbers 
which are too large to be used conveniently. We therefore 
describe the different colors by their wave-lengths in air, 
instead of by the number of vibrations per second. Violet 
light has a wave-length of about yoiro o" °f an mcn or 3 0*00 
of a millimeter, while the wave-length of red is about 4 qq 00 
of an inch or about y^nr of a millimeter. Differences in 
color are believed to be due to differences in wave-length. 

406. Invisible Spectrum. The ear can perceive sounds 
extending over perhaps 10 octaves, so that the shrillest 
audible note has a frequency 1000 or more times as great as 
the lowest. In contrast to this, the range of ether waves 
perceptible to the eye corresponds to less than one octave, 
since the longest visible wave-length is less than twice the 
shortest. Just as there are air-waves whose frequency 
is too high for the ear to perceive them, so there are ether 
waves of too great frequency to be seen. These are often 
spoken of as ultra-violet radiation. This radiation acts upon 
a photographic plate in the same manner as light, and falling 
upon some substances (notably a mineral called Wille- 
mite) causes them to glow. The last-mentioned phenome- 
non is called fluorescence. There are ultra-violet wave- 
lengths in radiation from the sun and from many artificial 
sources, especially the electric arc, in which, if iron rods 



CAUSE OF DISPERSION 201 

are used instead of carbon, a large part of the energy- 
developed has shorter wave-lengths than violet light. The 
term radiation is applied to any ether waves, whatever their 
wave-length. Those which are too long to be visible are 
classed as infra-red radiation and are often called heat- 
waves, because objects which absorb them are heated. 

407. Complexity of White Light. Dispersion is evidently 
due in some way to difference of wave-length. If white 
light were made up of an immense number of separate and 
distinct trains of waves of different wave-length, we might 
perhaps imagine how they could be separated from each 
other. They are not separate, however, but all the wave- 
lengths are parts of an infinitely complex train of waves, 
comparable to the noise of a boiler factory. Imagine 
passing such a train of sound waves through a device that 
would sort them into a succession of pure musical notes! 
Yet this is what the prism does to the white light. It picks 
the ether waves to pieces and sorts the parts with reference 
to wave-length. For the sake of simplicity we shall speak 
of the colors as if they had existed as separate things before 
the white light was dispersed. 

408. Cause of Dispersion. The cause of refraction is the 
difference in the speed of light in different media. Dis- 
persion may be ascribed to differences in the amount of 
hindrance which the different colors experience in travelling 
through a denser medium. ^ 
The shorter waves are hin- ^ 
dered in general more than 
the longer ones. The effect 
of this retardation is to 
cause the violet waves to FlG 2 30.-Dispersion by prism, 
be turned aside more than 

the red, for it is evident from the explanation of refrac- 
tion already given that the more a train of waves is 
slowed up in entering a new medium, the more will their 
direction be changed. In the diagram, imagine the beam 
of light falling on the prism to be made up of red and blue. 




& 



202 LIGHT 

The dotted lines represent blue wave-fronts and the solid 
lines red wave-fronts. After passing through the prism the 
red and blue beams will diverge, and at a distance from it 
will be quite separate. 

409. Pure Spectrum. When a beam of sunlight shines 
through a small hole, the round spot of light formed where 
the beam strikes the wall or floor is an image of the sun. If 
a prism is placed in the path of the beam, the spectrum that 
results consists of many overlapping round images of the sun, 
each of a different color. Because of the overlapping, the 
colors are more or less mixed. 

The arrangement shown in the „ 

diagram produces a spectrum r '^ A ^ 

in which the colors are not 
mixed. S is a narrow slit 
illuminated by sunlight. The . 

lens L is so placed as to give ,\ 

a sharp image of the slit on ^ 

a screen at / when the prism Fig. 231 

P is not in place. When the 

prism is introduced, the beam is turned aside, and if the 

screen T be placed in the path of the beam as far from the 

lens as /, we shall have upon it many colored images of the 

slit side by side, overlapping only very slightly. Such a 

band of colors is called a pure spectrum. 

410. Continuous Spectrum. If the light from a gas flame 
or any of the common artificial sources be passed through 
a prism, the spectrum which is obtained is similar to that of 
the sun in containing all the colors from red to blue. The 
relative intensity of the different colors will vary, but light 
from all the sources will give continuous spectra. This 
will be true of any source of light consisting of a glowing 
solid or liquid. In most forms of electric lights the source is 
glowing carbon. In the flame of a candle or oil lamp the 
light is also due to tiny particles of carbon in a glowing 
or incandescent condition. The presence of these particles 
of carbon may be shown by holding a piece of cold glass or 



THE SPECTROSCOPE 203 

porcelain in the flame for a few seconds. It will be blackened 
by a deposit of carbon. The spectrum of the light from 
white-hot and molten metals is also continuous. 

411. Bright Line Spectrum. Glowing gases, if they are not 
too much compressed, give spectra consisting of bright 
lines. The most often observed spectrum of this sort is 
that given by vapor of sodium, which may be obtained by 
dipping a wire or a piece of asbestos in a solution of salt and 
holding it in the flame of an alcohol lamp or the pale blue 
flame of a Bunsen burner. The salt is partly vaporized 
by the heat, and gives a yellow light, the spectrum of which 
consists of two yellow lines so close together that they often 
seem like one line. The molecules or atoms of sodium when 
in the gaseous state are free to give their own particular 
rate of vibration, just as bells of the same material, size, and 
shape all give the same note when struck if they are hung up 
so as to vibrate freely. If the bells were piled together 
and struck, the sound would be a jangle utterly unlike the 
note of the separate bells, and containing very many rates 
of vibration. So the light given by a glowing solid or liquid 
contains very many rates of vibration, because the mole- 
cules instead of being free to vibrate in their natural periods 
are crowded together and so send out an indefinitely great 
variety of waves. 

412. Absorption Spectrum. If white light be passed 
through heated sodium vapor, the vapor is set into vibration 
and so absorbs some energy from the complex waves which 
pass through it. Just as a tuning fork will select its own 
note from a jumble of sounds and respond to it, so from 
white light the sodium vapor takes up energy of its own 
particular wave-length. The light which has passed through 
the sodium vapor is thus deficient in yellow, and has a dark 
line at the precise place in the spectrum where the yellow 
line of sodium belongs. 

413. The Spectroscope. The yellow color given to the flame 
by sodium had been used by chemists as a means of detecting 
the presence of this element long before 1850. Character- 



204 



LIGHT 



istic colors given to the flame by other substances were also 
known; copper, for instance, giving green and strontium red. 
The instrument called the _, ~ 

spectroscope, used for ex- n/\ — ■ a ,. a & 

amining the spectrum of 

light from any source, was 

invented about 1856 by 

Bunsen 1 and Kirchhoff. 2 

The plan of one form of p IG 232.— Plan of spectroscope. 

simple spectroscope is 

shown in Fig. 232, and a view of the instrument in Fig. 

233. At opposite ends of a tube are the "collimating 





Fig. 233. — Spectroscope. 

lens" C and the narrow slit S, the length of the tube 
being such that the slit is at the principal focus of the 
lens. The light to be examined is placed at L. The illumi- 
nated slit now behaves like a source of light, and the lens C 

1 Robert Wilhelm Bunsen, 1811-1899, celebrated German chemist, 
Professor at Heidelberg, invented the Bunsen burner and, with 
Kirchhoff, the spectroscope. 

2 Gustav Robert Kirchhoff, 1824-1887, German scientist, associated 
with Bunsen in the invention of the spectroscope. 



SPECTRUM ANALYSIS 205 

sends out a parallel beam toward T, a small telescope focused 
for infinite distance. When the prism P is removed, this 
telescope gives to an eye at E a sharp image of the slit in 
its natural color. When the prism is placed as shown, the 
parallel beam is dispersed, and the telescope being moved 
to T", as many images of the slit will be seen as there are 
elementary colors in the light, each image being different in 
color from all the others. If L is a lamp flame, there will be 
an infinite number of images of the slit, and the observer at 
E f will see a continuous spectrum. If the source is a Bunsen 
flame with some common salt in it, there will be a very 
faint spectrum due to the pale blue Bunsen flame, with a 
bright yellow line, or two lines. Other substances will give 
characteristic spectra; those containing sodium, potassium, 
lithium, strontium, calcium, barium, and thallium being 
particularly well adapted for the mode of observation de- 
scribed. 

414. Spectrum Analysis. Every element has its own 
characteristic spectrum. Many compounds of the seven 
elements mentioned in last paragraph are partly rendered 
gaseous at the temperature of the Bunsen flame, and give 
bright line spectra. Others require a higher temperature. 
By means of the electric arc (paragraph 669), compounds 
of the heavy metals or the metals themselves may be vapor- 
ized and so give their characteristic bright line spectra. 
The spectrum of copper can be shown by using copper 
rods instead of carbons in an arc lamp. The same is true 
of iron and some other heavy metals. 

The "b right line spectra of the elementary gases, oxygen, 
hydrogen, etc., are obtained by passing electric sparks 

through them. For this pur- ■ . . 

pose the gases are sealed into ° v j v, Z7° 

glass tubes of the shape Fig 234.— Pliicker tube, 

shown in Fig. 234, having 

platinum wires fused into the glass. When a powerful elec- 
tric discharge takes place between the terminals, the gas in 
the narrow part of the tube is heated to incandescence. 



206 LIGHT 

415. No two of the elements have any spectrum lines in 
common. This fact makes the spectroscope valuable in 
determining what elements are present in a substance, be- 
cause when it has once been determined what lines an ele- 
ment gives, any of those lines in a spectrum will show the 
presence of that element. One of the earliest triumphs 
of the spectroscope was the discovery of a new element. 
A dark red line not belonging to any known element was 
observed in the spectrum of a substance obtained from 
the water of a mineral spring. This showed the presence 
of a new element, which was soon after separated and 
named rubidium, from the red line. Caesium was discovered 
in the same manner. A line having been observed in the 
solar spectrum corresponding to no known element, the 
element giving it was named helium (Greek helios, the sun). 
Many years later helium was found in analyzing a rare 
mineral. It is a very light gas, and occurs in very minute 
quantities on the earth, but it must be very abundant in 
the atmosphere of the sun. 

416. Spectra of the Sun and Stars. The helium line in the 
solar spectrum, above referred to, was a bright line, ob- 
served during an eclipse in examining the light of the solar 
prominences which project so far out from the sun as to be 
visible during a total eclipse. It had long been known that 
the spectrum of the sun contains many dark lines. Bunsen 
and Kirchhoff showed that many of these lines correspond 
exactly to lines in the spectra of iron, barium, sodium, 
hydrogen and other familiar elements. These elements 
must be present as vapors in the sun's atmosphere. White 
light from the incandescent materials below shines through 
the vapors, and an absorption spectrum is produced, crossed 
by many dark lines. The spectra of many of the stars 
are similar to that of the sun. Some stars and many 
nebulae give bright line spectra. 

417. Three Classes of Spectra. Nearly all spectra belong to 
one of the three classes that have been described. 



ACHROMATIC PRISM 



207 




Fig. 235. — Chromatic aberration. 



Continuous spectra are given by light from a glowing solid, 

liquid or compressed gas. Bright line spectra are those of 

incandescent gases under rather low pressure. Dark line, 

yor absorption spectra, are produced when white light shines 

through a glowing gas (or through certain solids and liquids). 

418. Chromatic Aberration of Lenses. When parallel white 
light falls on a lens L, the violet waves are more refracted 
than the red, and so are 
brought to a focus nearer to 
the lens The principal focus 
for the violet rays is shown 
at V and that for the red at 
R. This effect is called chromatic aberration. It causes 
telescopes and other instruments made with single lenses to 
form images having colored fringes. 

419. Differences in Dispersive Power. The index of re- 
fraction of heavy flint glass for red light is about 1.62 and 
for violet about 1.66. That is to say, the violet is refracted 
more than the red by an amount corresponding to a differ- 
ence of .04 in the refractive indices. Soft crown glass has 
an index of about 1.51 for red and 1.53 for violet, the 
difference being only .02. These facts are briefly expressed 
by saying that the flint glass has twice as much dispersive 
power as the crown glass. 

Achromatic Prism. The average refractive power of flint 
glass is greater than that of crown glass, but the contrast 
is far less than in their powers of dispersion. If a prism of 
crown glass be combined as in 
the figure with one of flint having 
half the angle, a beam of light 
passing through the two will 
have its colors scarcely sepa- 
rated at all, since the dispersion 
of the crown glass is corrected 

by the flint. The direction of the beam will be changed, 
however, since the total refractive power of the flint prism 
is less than that of the crown. 




208 



LIGHT 



420. Achromatic Lenses. The chromatic aberration of a 
crown glass convex lens can be corrected for any two colors 
by combining with it a concave lens of 
flint glass whose dispersive power for those 
two colors is the same as that of the con- 
vex lens. Such a combination gives an 
almost perfectly colorless image, and is 
called an achromatic lens. Most lenses used 
in optical instruments are of this type. 
Sometimes the two parts are cemented 
together with Canada balsam, whose 
refractive index is about the same as that of crown 

Newton believed achromatic lenses to 
For this reason he constructed a telescope having a concave 
mirror as its objective, since mirrors do not disperse light. 

421. The Rainbow. A ray of light entering a rain-drop in 
the direction shown in the figure is refracted at A, totally 
reflected at B, and again refracted at C. The solid lines 
represent the path of the red, and the dotted line that of the 
violet. It is evident that a drop in a certain position, 
catching the sunlight, would send a flash of red to the eye 
of an observer. At the same instant a drop a little lower 
down would send a flash of violet, and intermediate drops 
would send the intermediate colors of the spectrum. The 
angle between the incident and refracted rays in Fig. 238 



n 



h 



Fig. 237.— Achro- 
matic lens. 

glass, 
be impossible. 





Fig. 238 



Fig. 239 



is about 42 degrees for red and 40 degrees for violet. In 
Fig. 239, suppose the sun just setting, so that its rays are 



COMPLEMENTARY COLORS 



209 



parallel to the horizon. A and B are two drops which are re- 
flecting violet rays to an observer at E. All drops on a 
conical surface having its apex at E and making an angle of 
40 degrees with the axis EO will send violet light to the eye. 
As fast as one set of drops fall past the proper point, others 
take their places. In like manner other drops are sending 
the other colors, and the appearance to the eye of the 
observer is that of an arch whose centre is opposite the sun. 
The colors are brighter in proportion as the number of drops 
falling is larger. When the sun is just setting the bow is a 
semicircle. Otherwise it is a smaller arc. 

422. The Secondary Bow is formed by light which has suf- 
fered two reflections and two refractions. Fig. 240 shows 
the course of a ray through 
the drop, the dotted line 
being the violet part and 
the solid one the red. In 
this case the violet forms 
the outside of the bow. 
The secondarjr bow is much 
fainter than the first because so much less light enters 
the drop at A on account of the large angle of incidence. 
This bow is only noticed when the primary bow is very 
bright. The angle ROR r is 51 degrees, so the secondary 
bow appears outside of the primary. 

423. Complementary Colors. Not only is the impression of 
white produced by a mixture of all the elementary colors, 
but by various combinations of two or more of them. It is 
possible to select a blue and a yellow 

light which when thrown upon the same Y J& 

white surface will give the impression of j£° 
pure white. This is best done by direct- 
ing blue and yellow beams from two 
projecting lanterns upon the same 
screen. It may be done also by placing L° 
two lights, L L, so as to shine upon a 
white screen S and then placing a 
14 




B 

Fig. 241 



210 LIGHT 

blue glass in front of one light and a yellow one in front 
of the other. If the colors are properly chosen and the 
intensities of the lights correctly adjusted, the screen will 
appear white. The same result may be obtained with red 
and green. Such pairs are called complementary colors. 

424. Colors of Transparent Objects. Blue glass appears 
blue because when white light falls upon it, it absorbs 
yellow and perhaps some others, the remaining colors com- 
bining to form blue. We may determine what colors the 
blue glass transmits by passing the light which has traversed 
the glass through a prism. It will generally be found that 
violet, blue, and green are transmitted by blue glass. Yellow 
glass, examined in the same manner, will be in general found 
to transmit also green and red. If white light fall upon blue 
and yellow glass in succession, the light transmitted by both 
will be green. 

425. Colors of Opaque Objects. When white light falls 
upon an opaque object, some of it is absorbed and some 
reflected. The color of such a body is determined therefore, 
as in the case of transparent things, by its selective absorp- 
tion. If it absorbs red and reflects all the other colors it 
appears green. We may make an approximate analysis 
of the color of an opaque object by holding it successively 
in the various parts of a continuous spectrum. A strip of 
blue paper will probably look violet in the violet end of the 
spectrum, blue in the blue, and green in the green, but when 
placed in the yellow part of the spectrum it will appear black. 
In the same manner a deep yellow paper reflects green, 
yellow, and red, but shows no color in the blue. These results 
explain why blue and yellow paints mixed make green. 
White objects reflect all colors equally, and black ones absorb 
almost all the light that falls on them. 

426. Newton's Disc. If properly selected colors be ar- 
ranged on a disc and the disc rapidly rotated (Fig. 242), 
the images of the parts will be blended in the eye, and the 
disc will appear white or gray. The gray is perhaps due to 
insufficient illumination. This mode of recomposition of 




COLOR-SENSE 211 

white is due to Newton. If the red sectors be covered by 
black paper and the disc rotated, the remaining colors blend 
to form green. In the same manner, 
if any color be covered, the rest blend 
to form its complementary. 

427. Colors in Monochromatic Light. 
If we attempt to sort a lot of bright- 
colored objects in sodium light, we 
find it impossible to distinguish reds 
and greens. They both appear gray. 
If the sodium light is made by hold- 
ing in a Bunsen flame the end of a 
glass tube that has been heated and FlG 242.— Newton's disc 
dipped in salt, we shall be able to see 

the blues very faintly, because of the pale blue of the Bunsen 
flame which is present in the light. In a general way, things 
which cannot reflect yellow show no definite color in such 
light. 

428. Colors as seen in the red light of a photographic 
dark-room are very much modified, although the light is not 
entirely monochromatic. The difficulty of naming colors 
correctly in the light from gas or kerosene is another illustra- 
tion of the fact that objects cannot reflect colors which they 
do not receive, and therefore we can get correct impressions 
of many colored things only by seeing them in white light. 

429. Color-sense. It is not always possible to tell by the 
eye alone what colors are present in composite light, since 
the same effect may be produced by different causes. It 
has already been mentioned that the same sensation as that 
produced by white light may result from a mixture of two 
colors. All compound colors may be imitated, so far as our 
sensations go, by combining in the proper proportions three 
colors, which may be roughly described as red, green, and 
violet. It is supposed that our color sensations are given 
by three sets of nerve-termini, each of which is sensitive to one 
of the three colors mentioned, which three are sometimes 
called primary colors. 



212 



LIGHT 



430. Color-blindness. Some persons cannot distinguish red 
objects from green ones. More rarely we find a person who 
confuses yellow and blue. Such an eye is believed to be 
deficient in one of the sets of nerve-termini which are present 
in the normal eye. 

431. Colors by Contrast. If a spot of green light and one of 
white be thrown on a screen side by side, the white one 
appears red, and in general a patch of colored light makes 
the adjacent white patch appear of the complementary color. 
Another experiment on color sensation is easily tried and 
striking, but physics does not explain it. Look intently for 
a minute at a brightly illuminated object of brilliant color. 
Then look at a white surface. An image of the object will 
appear on the white surface, but with the complementary 
color. 

INTERFERENCE OF LIGHT. 

432. It has been stated (paragraph 282) that light waves, 
like other waves, are capable of interference. As in the 
case of sound waves, we must have two sources whose 
vibration frequency is the same or nearly so, in order to 
observe satisfactorily the phenomena of interference. 

433. Fresnel's Bi-prism. One method of producing inter- 
ference is shown in Fig. 243. A sodium light is placed at A 




Fig 243 



behind a slit S. At BC are two thin prisms base to base, 
called a bi-prism. The light after passing through the 
prism falls on the surface ON" or on the objective of a tele- 



AIR-PRISM 



213 



scope. Consider the light that falls at 0, in the axis of the 
instrument. The rays arriving at this point have traversed 
similar paths, so that the waves which started in the same 
phase arrive in the same phase and reenforce each other. 
At another point, as N, however, rays arrive by dissimilar 
paths, and because one of them has traversed a greater 
thickness of glass it has been delayed. We may imagine 
the light to come, as it seems to, from P and P', and disregard 
the bi-prism. Then we may say that the ray from P' 
arrives later because it has farther to come. If this delay 
amounts to a half wave-length, there will be destructive inter- 
ference at N, and a dark line results. At N', twice as far 
from 0, the difference of path amounts to a whole wave- 
length, and the waves from the two sources will again re- 
enforce each other. At N" the difference is 1^ wave-lengths, 
and interference again occurs. Thus there will be a succes- 
sion of light and dark bands on both sides of 0. 

434. Air-prism. A beautiful method of showing inter- 
ference is by means of the air-prism shown in Fig. 244. 
Two pieces of heavy plate glass are held together at one edge 
and at the other separated a very small distance by a strip 
of thin paper. Sodium light reflected 
from either face of this gives interfer- 
ence bands because of the interference 
of the light reflected from the two sur- 
faces AB and AC. Suppose light enter- 
ing from the right. At a point where 
the plates are together there will be 
a dark band, since change of phase 
takes place in reflection from the 
glass surface AB, and none in reflec- 
tion from the air surface AC. This 
change of phase produces in effect a detention of a half 
wave-length in the light reflected from the glass surface. 
Where the glass plates are j wave-length apart the two 
trains of reflected waves will be in coincidence, and there 
will be a bright band. Where the distance is \ wave-length 



Fig. 244. — Air-prism. 
(Distance BC very much 
exaggerated.) 



214 LIGHT 

there will be a dark band, and at J wave-length distance 
another bright one, and so on. 

435. Colors in Thin Films. If white light be reflected 
from the apparatus last described, the different colors will 
interfere at different points. At A all colors are quenched. 

Where the distance between the ^ 

plates is 2 wave-length ol red, the ( w////^^ . ■ 

red will be quenched, and we shall p IG 245 

have a green band. Thus are pro- 
duced bands of color instead of simply light and dark bands. 
Newton used a lens of small curvature and a plane piece of 
glass (Fig. 245). This apparatus gives concentric rings of 
color when viewed in white light. 

The colors we see in soap bubbles are due to the inter- 
ference of light reflected from the two surfaces of the film. 
The colors shown by mother-of-pearl are among the many 
familiar instances of color produced by interference. The 
substance is built up of very thin partly transparent layers. 

436. Diffraction. Sound waves bend around corners. 
Light waves do the same, but to a very much smaller extent. 
When light passes through a narrow slit, the edges of the 
slit, being centres of disturbance, behave like sources of light, 
and the waves from the two edges interfere. This bending 
of trains of light waves is known as diffraction. Diffraction 
occurs also at a single edge, and makes absolutely sharp 
shadows impossible. 

437. Diffraction Grating. If, instead of one slit, many 
parallel ones are used, the amount of light passing through 
and suffering diffraction and interference may be sufficient to 
give brilliant spectrum colors. Such an arrangement, made 
by ruling close parallel lines on glass with a diamond point, 
is called a diffraction grating. Gratings 1 are also made on 
speculum metal, and give spectra in the reflected light. 
The lines are often as close together as .002 of a millimeter. 

1 Photographs of gratings answer well for many purposes. Excellent 
copies of speculum metal gratings impressed on celluloid are now made. 




DOUBLE REFRACTION 215 

Gratings are more satisfactory than prisms for accurate 
spectroscopic work, because equal distances between lines 
in the diffraction spectrum denote equal differences of wave- 
length. In a prismatic spectrum this is not the case; the 
violet is drawn out more than the red, making the lines rela- 
tively farther apart. The spectrum made by a grating is 
called a normal spectrum. 

POLARIZATION. 

438. Ordinary light consists of waves in which the dis- 
turbances take place in all planes passing through the direc- 
tion in which the light is travelling. This may be illustrated 
by fastening a rope at one 
end and whirling it after ^_ 
the fashion of a jumping 
rope. From any point of 
view the rope seems in 

vibration. But if the rope, tied at A and whirled by a hand 
at C, is confined by a slot B, the part between A and B 
will vibrate only up and down, while that from B to C will 
vibrate in all planes as before. 

439. Polarization by Tourmaline. Something very like 
this happens to light which has passed through a thin 
slice of tourmaline crystal. Instead of vibrating in all 
planes, its vibrations are confined to one plane, like the rope 
from A to B, and is said to be plane- 
polarized, or more simply polarized. Such H 
light will pass through a second piece of I 
tourmaline whose axis is parallel to that "H 
of the first, but if the axes are perpen- Fig. 
dicular, no light gets through. If two 

slots at right angles to each other were placed at B, Fig. 246, 
the part AB would not move at all, and the crossed tour- 
malines have the same effect on the light. 

440. Double Refraction. A beam of light in passing through 
clear Iceland spar (crystallized carbonate of lime) is broken 





216 LIGHT 

up into two beams, both of which are polarized. The planes 
of polarization are at right angles to each other. Many 
other crystalline substances are doubly refracting, but none 
to such a marked degree 
as Iceland spar. The 
light which shows the 
same index of refraction 
for all angles of incidence, 
and which passes perpen- 
dicularly through the 
crystal, is called the ordi- 
nary ray. The other is 
the extraordinary ray. It FlG - 248.-Double refraction by Ice- 
seems that the crystalline an spar * 
structure of these bodies (or as we may say, their molecular 
arrangement), is such as to subject the ether contained in 
them to some sort of a strain. This limitation of the freedom 
of the ether may be the cause of the polarization of trans- 
mitted light, as well as of double refraction. 

441. Rotation of the Plane of Polarization. Some substances 
in transmitting polarized light cause the plane of polarization 
to rotate; twist it around, so to speak. Mica is one of these 
substances which are said to be optically active. A piece 
of mica of the proper thickness may be so placed between 
crossed tourmalines as to rotate the plane of polarization 
90 degrees, and so enable the light to pass through the second 
tourmaline, thus restoring the light. 

442. Polariscope Tests for Sugar. A solution of sugar has 
the power of rotation, some sugars causing the plane of polar- 
ization to revolve in one direction and some in the other. 
The polariscope, an instrument for measuring the amount and 
direction of this rotation, is used in testing sugars. 

EXERCISES. 

1. Some stars have dark-line spectra, and some have bright- 
line spectra. What may be inferred in regard to their 
relative temperatures? 



EXERCISES 217 

2. In steel-making the impurities are burned out of the 
molten steel. The flame is watched with a spectroscope. 
Suggest a reason for this. 

3. Why do rainbows not occur near the middle of the day? 
Why are they much more common in the evening than in 
the morning? 

4. How can it be proved that the moon and planets shine 
by reflected sunlight? 

5. Why do people's faces look ghastly in sodium light? 

6. The statement is sometimes made that no two persons 
see the same rainbow. Is this true? 

7. An arch of color is often seen in the spray from a water- 
fall. Is this a true rainbow? 



CHAPTEE VIII. 

HEAT. 

443. Sensation of Heat. The nerves which give us the 
sensations of hot and cold are distributed over the whole 
surface of the body. So far as our sensations are con- 
cerned, therefore, no definition of heat is necessary. 

444. Heat a Form of Energy. What is the physical differ- 
ence between a hot body and a cold one? For a long time 
this difference was supposed to be due to the presence in the 
hot body of a substance called caloric. Because heating a 
body does not in general change its weight, caloric was 
believed to be " imponderable." The phenomena of heat 
were accounted for very ingeniously, but by the end of the 
eighteenth century it had become clear to a number of 
scientists that heat is not a substance. Among these perhaps 
the most notable were Count Rumford 1 and Sir Humphry 
Davy. 2 Count Rumford had made the very common observa- 
tion that boring tools become hot while in use. In the arsenal 
at Munich, cannon were bored by horse-power, and great 
quantities of heat were generated. Rumford placed a mass 
of metal weighing more than a hundred pounds in water 
and brought to bear upon it a blunt boring tool turned by 
a horse. Nearly twenty pounds of water were raised from 
60° F. to the boiling point in two hours, about half a pound 
of metal having been worn off. He concluded that since an 

1 Benjamin Thompson, distinguished scientist, born in America, 
1753. Made Count Rumford by the King of Bavaria. Died 1814. 

2 Sir Humphry Davy, 1778-1829, illustrious English chemist, dis- 
coverer of the electric arc, and of the metals potassium and sodium. 
Invented the miner's safety lamp. 

(218) 



TEMPERA T URE 219 

unlimited quantity of heat can be obtained from the same 
piece of metal, heat must be some kind of motion. 

445. A few years later Sir Humphry Davy melted two 
pieces of ice by rubbing them together. He announced his 
conclusion in 1812, that "the fundamental cause of the 
phenomena of heat is motion." This view won its way but 
slowly, and the demonstration of the kinetic theory was 
not completed until 1843, when Joule 1 showed that a definite 
amount of work done produces a definite amount of heat. From 
the point of view of the doctrine of the conservation of energy, 
this is equivalent to saying that heat is a form of energy. 
This fact has already been mentioned. We now believe 
that heat-energy is due to motion of the molecules, and that 
the molecules of a heated body execute very small and very 
rapid vibrations. 

446. Sources of Heat. It has been already stated that all 
other forms of energy tend to degenerate into heat. The 
most common artificial source is chemical action, of the 
particular kind which we call combustion. We burn coal, 
wood, or gas to cook our food and warm our houses. The 
human body is kept warm by the oxidation of the waste 
products of the body by the air we breathe. If one works 
hard, he uses up tissue faster, breathes more rapidly, and 
feels warm because of the more rapid combustion going on 
in his body. 

447. Temperature. If an object which we touch is not so 
warm as the hand, we say it is cool or cold, depending on 
the amount of difference ; if it is warmer, we say it is warm, 
or if it gives pain it is hot (or may be very cold). For several 
reasons we cannot tell accurately how warm or cold a thing 
is, but we say in a general way that the bodies differ in tem- 
perature. Here again we have a term difficult of definition 
because the idea is so fundamental. Temperature in the 
case of heat is analogous to difference of level in the case of 

1 James P. Joule, 1818-1889. English physicist. His most notable 
work is on the mechanical equivalent of heat. 



220 HEAT 

water. If two vessels are so arranged that water flows from 
one to the other, we say that the one from which water flows 
is at a higher level. So if two bodies at different tempera- 
tures are placed in contact, heat flows from the body at 
higher temperature to that whose temperature is lower. 
An object feels warm to the touch when heat flows from it 
to the hand. It feels cool when the flow is in the opposite 
direction. Thus the same object may feel cool to a person 
whose hand is at its ordinary temperature, and warm to one 
whose hand is cold. 

448. Thermometers are used to measure differences of 
temperature. They usually do this by means of the expan- 
sion of some substance. Nearly all substances 
expand when heated, and in most instances the 
amount of expansion is nearly proportional to the 
rise of temperature. A model of the ordinary 
thermometer may be made from a flask, a straight 
piece of glass tube, a cork and some water. The 
water should be colored so as to be more easily 
visible in the tube, which fits tightly in a hole in 
the cork. The flask is filled quite full of water 
and the cork pushed in so far as to raise the water 
some distance in the tube. If the flask be now 
heated, the top of the column a will rise in the 
tube, because the water expands with rise of Fig. 249 
temperature. Such a device is a water thermometer. 

449. Mercury Thermometers are much the most common. 
The reasons for using mercury in preference to other liquids 
are several. It is opaque, so that a slender column of it 
is easily visible. It freezes at a very low temperature and 
boils at a very high one. It expands with almost perfect 
uniformity. For very low temperatures, alcohol is used; 
also in certain special forms of thermometers, and, on account 
of its cheapness, in some very large ones. The bore of the 
tube of a thermometer must be as nearly uniform as possible. 
It is often made flat, so that a very slender column may be 
spread out and be seen more easily. Sometimes it is made 




THERMOMETER SCALES 



221 



© 

Cross- section 
of thermome- 
ter tube. 




E 

Magnifying 
front thermo- 
meter tube. 
Fig. 250 



with a " magnifying front." The glass of the tube is a 

cylindrical lens which magnifies the width of the column 

but not its length. Both forms 

are shown in Fig. 250. The 

lines show how the lens front 

magnifies. 

450. Thermometer Scales. The 
series of horizontal marks placed 
on or behind the tube of the ther- 
mometer form the scale. The 
freezing point of water is the 
temperature from which measure- 
ments are made. This and the 
boiling point are called " fixed 
points" because under the same 
conditions water always freezes at the same temperature 
and boils at the same temperature. Many scales have been 
devised, but only three are now used to any extent : these are 
the Fahrenheit, Centigrade, and Reaumur. The first is com- 
monly used in England and America, the second in France, 
Spain, and Italy, and the third in Germany and Russia. 
The Centigrade scale is generally used in scien- 
tific work, everywhere. On it the freezing 
point is marked 0° and the boiling point 100°, 
and the space between is divided into one 
hundred equal spaces called degrees (abbrevi- 
ated to ° ). Additional degrees of the same 
length are made above 100° and below 0°. 
The Reaumur scale has 0° at the freezing point 
and 80° at the boiling point, while the Fahren- 
heit has its freezing point at 32° and its boiling point at 212°. 
Temperatures as low as — 39° C. may be measured with the 
mercury thermometer. For lower temperatures alcohol is 
used. The boiling point of mercury is 357° C, but tempera- 
tures up to about 500° C. may be measured by filling the tube 
with compressed nitrogen or some other gas which does not 
act on mercury, and using a strong bulb of hard glass. 



P. c. 

B0 100 



o c 



32 

FREEZING 



o 



Fig 251 



222 



HEAT 



M2Q 
M20 



451. Comparison of Scales. Fig. 252 shows some points of 
comparison on all three scales. It is clear that 100° on the 
Centigrade scale occupy as much ^ «, „ 

space as 80° on the Reaumur, and 
212°— 32° =180° on the Fahrenheit. 
In length, therefore, 1 Centigrade 
degree = f of a Reaumur degree or 
f of a Fahrenheit degree. In order to 
express Reaumur temperatures as 
Centigrade temperatures or vice 
versa, the ratio is the only thing we 
have to consider. Thus 17° C. = f 
X 17° R. = 4p = 13f ° R. Also, 
60° R. = f X 60° C. = 75° C. When 
we wish to express a Fahrenheit tem- 
perature in either of the other scales, 
we must take account of the differ- 
ence in the zero points. Thus 20° C. 
= f X 20° F. = 36° F. above the 
freezing point. Therefore the tem- 
perature on the F. scale correspond- 
ing to 20° C. is 36° + 32° = 68° F. 
A temperature below the freezing point on the C. scale is 
indicated by a negative sign; on the F. scale negative tem- 
peratures are those below the Fahrenheit zero. — 20° C. = 
36° F. below the freezing point, or 4° F. below 0° or — 4° F. 




Fig 252. — Thermometer 
with three scales. 



PROBLEMS. 



1. Express the following as Fahrenheit temperatures: 
60° C; 21° C; —10° C; —40° C; 8° R. 

2. Express the following as Centigrade temperatures: 
70° F.; 98f F.; 10° F.; 0° F.; 29f R. 

452. Expansion of Solids. The fact that metals expand 
when heated is illustrated by the simple apparatus shown 
in Fig. 253. The metal ball will just pass through the ring 




COEFFICIENT OF LINEAR EXPANSION 223 

when they are at the same temperature. If the ball be heated 
it will not pass through at first. Presently, the ring having 
risen in temperature and the ball fallen, it again passes 
through. The blacksmith heats 
the tires of wheels before putting 
them on, and in cooling they 
shrink and draw the wheel 
tightly together. In steel truss 

bridges, one end of a span is FlG 253 _ Ball and rm ^ 

fastened to the pier and the 
other rests on rollers, that it may expand and contract with- 
out damage. Telegraph wires are tighter in cold weather. 

453. Coefficient of Linear Expansion. For the same dif- 
ference of temperature different solids expand or contract 
very unequally. In order to compare them in this respect 
we must measure the expansion of a certain length of the 
solid for a certain rise of temperature. It is customary to 
measure the expansion of a long piece of the solid due to a 
rise of many degrees of temperature and then calculate the 
elongation of one unit length for 1° rise. For instance, a 
rod of aluminum 600 mm. long expanded 1.1 mm. in length 
in rising from 20° C. to 100° C. An expansion of 1.1 mm. 
for 80° rise gives .01375 mm. for 1° rise. Then if 600 mm. 
expanded .01375 mm. for 1°, 1 mm. would expand -g-J-g- of 
.01375 or .0000229 mm. We here assume that the expan- 
sion is the same for each degree rise of temperature, and this 
is very nearly true. The ratio of the expansion for 1° C. 
to the length of the rod at 0° C. 1 is called the coefficient of 
linear expansion. Or we may say the coefficient of linear 
expansion is the fraction of a millimeter which a rod of the 
substance one millimeter long expands for one degree rise of 
temperature. This for aluminum is about .000023. Values 
for other solids are given in the table, page 227. 

1 The divisor used in finding the coefficient is usually the length at 
the temperature of the room, giving practically the same result as if 
we used the zero length. 



224 



HEAT 



454. Dial Thermometers make use of difference in rate 
of expansion. The principle is shown in Fig. 254. A bar 
of steel and one of brass are fastened together by the process 
known as brazing. When the temperature of this compound 
bar rises, the brass expands more than the steel, and the 
bar bends. One form of the dial thermometer has a spiral 
made of a slender compound bar. Change of temperature 



A 




Fig. 254 — Compound bar: 
A, cold; B, hot. 



Fig. 255. Metallic thermometer. 



causes the spiral to uncoil or coil up. It is fastened at one 
end, and at the other is connected with a pointer which 
moves over a dial. Fig. 255 shows one form of the in- 
strument. In the form commonly used the dial is vertical 
like that of a clock, and the mechanism is behind the dial 
and so concealed. The same principle is used in some self- 
recording thermometers or ' thermographs/' 

455. Compensating Pendulums. If the pendulum of a 
clock becomes longer, the clock " loses time," since each 
swing takes a longer time than before expansion. One 
method of preventing the pendulum from elongating is 
shown in Fig. 256. The steel pendulum rod a carries at its 
lower end a frame, b, which supports a tall jar of mercury, c. 
The mercury column in the jar increases in length with 



COEFFICIENT OF CUBICAL EXPANSION 



225 



rise of temperature more than ten times as much as the steel 

rod does. By properly adjusting the depth of mercury in 

the jar, the expansion of 

the mercury upward may 

be made to counterbalance 

the expansion of the steel 

downward, and so keep 

the centre of oscillation 

at the same distance from 

the centre of suspension 

at all temperatures. 

456. In the " gridiron" 
pendulum, the steel rods 
a, b, and c are fastened at 
the upper end and expand 
downward, while the brass 
rods d and e are fastened 
at the bottom and expand 
upward. Their lengths are 
so adjusted as to keep the 




Fig. 256.— Mercury 
compensation pendu- 
lum. 



Fig. 257.— 
Gridiron pen- 
dulum. 



bob from rising and falling with change of temperature. 
Balance wheels of watches are " compensated" by means 
of compound bars. An alloy called " invar" is now being 
used to some extent in the making of pendulum rods. 
Its coefficient of expansion for ordinary house tempera- 
tures is practically zero, so that no compensation is neces- 
sary. 

457. Coefficient of Cubical Expansion. Suppose a cube of 
aluminum whose edge is 1 cm. long at 0° C. At 1° C. the 
length of the edge would be 1.000023 cm., and the volume 
would be (1.000023) 3 cc. = 1.000069001587012167 cubic 
centimeters. Neglecting the decimal places 
beyond the eighth, the volume of the cube 
would increase .000069 of itself for 1° C. rise 
of temperature. This increase, which is called 
the coefficient of cubical expansion, is three times 
the linear coefficient. Let Fig. 258 represent the 
15 




Fig. 258 



226 HEAT 

cube. A rise of 1° increases the length of the edge a .000023 
cm., and the increase in volume due to this expansion may be 
represented by a layer .000023 cm. thick on the top, having 
a volume of .000023 cc. Similarly, the increase in length 
of the dimensions corresponding to the edges b and c results 
in increased volume which may be represented by like 
layers added on the faces h and g. The sum of these three 
layers, with a total volume of .000069 cc, represents the 
entire increase in volume except the very minute strips on 
the edges a, b, and c, and at the corner o, which correspond 
to the parts of the decimal fraction that were rejected above. 

458. Expansion of Liquids. It is clear that we can consider 
only cubical expansion in the case of liquids and gases. In 
general, liquids expand more than solids. If the mercury 
in the bulb of the thermometer expanded no more rapidly 
than the glass of the bulb, the mercury would not rise in 
the tube with increase of temperature. If the bulb of the 
water thermometer (Fig. 249, p. 220) be suddenly immersed 
in ice-water, having been at the temperature of an ordinary 
room, the column in the tube will at first rise, because the 
glass is first cooled by contact with the ice-water and 
its shrinkage forces the water up the tube. In a few 
moments the water cools enough to cause the column to 
fall, and it will fall much farther than it rose. If the water 
thermometer be dipped into hot water, the column at first 
falls and then rises. 

459. We often observe changes of volume with changing 
temperature of liquids. A jar of preserves, filled quite 
full when boiling hot, will when cold have a considerable 
vacant space at the top. 

460. Expansion of Gases. Gases differ from liquids and 
solids in that they all have the same coefficient of expansion. 
Boyle's law (paragraph 232) shows the relation of volume 
to pressure in the case of a gas. The relation of volume and 
temperature is expressed in the Law of Charles: 1 Under 
constant pressure a mass of gas expands -^^ of its volume 

1 J. A. C. Charles, French scientist, 1746-1823. 



ABSOLUTE ZERO 



227 



at 0° C. for each Centigrade degree rise of temperature. 273 
cc. of air at 0° would become at 1°, 274 cc; or at — 1°, 
272 cc. if the pressure remained unchanged. If the law of 
Charles held absolutely without limit, the volume at — 273° 
would become zero. The law docs not hold with accuracy 
except within rather narrow limits, and at very low tempera- 
tures the variation is large. Long before — 273° is reached 
the gas becomes a liquid and even a solid. 

461. Absolute Zero. If 273 cc. of air at 0° and atmospheric 
pressure be placed in a sealed vessel of 273 cc. capacity, 
the air would exert a pressure of 1 atmosphere outward on 
the vessel. If now the temperature be reduced to — 136.5° 
C, the pressure upon the inside of the vessel would mani- 
festly be reduced to \ an atmosphere, and at — 273° C. 
the air in the vessel would exert no pressure whatever. That 
is, it would have no vibratory molecular motion; its heat 
would be zero. The absolute zero of temperature is therefore 
believed to be —273° C. 

In estimating density of gases they are always referred 
to standard conditions, i. e., a pressure of 760 mm. of mercury 
and temperature 0° C. 

Table of Coefficients of Expansion. 

Substance. Linear. 

Aluminum 000023 

Copper 000017 

Iron (or steel) 000011 

Lead 000029 

Platinum 000009 

Silver 000019 

Tin 000022 

Zinc 000029 

Brass 000019 

Glass 000009 

Ice 000037 

Air and other gases 

Alcohol at 0° C 

Mercury 

Kerosene 

Water at 20° C 

Water at 35° C 

Water at 50° C 

Water at 75° C 



Cubical. 
. 000069 
.000051 
. 000033 
.000088 
.000027 
.000058 
.000067 
.000087 



. 00367 
. 00104 
.00018 
.00099 
.00021 
. 00034 
. 00047 
.00064 



228 HEAT 



PROBLEMS. 



1. A rod of steel 600 mm. long expanded .5 mm. in being 
heated from 20° C. to 100° C. Determine its coefficient 
of linear expansion. With rods of the same length, heated 
through the same range, the following elongations were 
observed. Compute the coefficient in each case: Copper, 
.81 mm.; zinc, 1.39 mm.; tin, 1.05 mm.; Glass, .39 mm. 

2. A metal vessel is filled with gas at 0° C. at a pressure 
of 1 atmosphere, and sealed. The temperature of the 
vessel is then raised to 273° C. What is now the pressure 
within the vessel? 

3. The height of the column of mercury in a barometer is 
760 mm. out of doors at 0° C. Another barometer in a 
room at 20° C. will show what height at the same time, 
the reservoirs of the two barometers being at the same level T 

4. A steel bridge span is 50 meters long at 30° C. What 
will be its length at —20° C? Another is 100 feet long at 
—30° C. What is its length at 50° C? 

5. A mass of gas at 0° C. has a volume of 546 cc. What 
will be the volume at 20° C, the pressure remaining 
unchanged ? 

6. The volume of a mass of air at — 10° C. is 789 cc. 
With pressure unchanged what will be its volume at 20° C? 

7. 646 cc. of air at 50° C. will contract to what volume 
at 20°, under the same pressure? 

8. The volume of a mass of air at 20° C. and 760 mm. 
pressure is 586 cc. What will be its volume at 60° C. and 
750 mm. pressure. Solution: The volume at 20° is -^fy 
greater than it would be at 0° under the same pressure, 

-= |^-| of the zero volume. Therefore 586 cc. = -f-^f of zero 
volume, and the volume at 0° and 760 mm. would Be 586 

^ 2 9 3 = 546 cc At 60 o t hi s W ould be increased to fff X 
546 cc. = 666 cc, if the pressure remained unchanged. 
But the barometer having fallen from 760 mm. to 750 mm., 
the volume will be ^-f of what it would be at 760 mm., 
= 674.88 cc. 



SPECIFIC HEAT 229 

9. 1132 cc. of air at 10° C. and 750 mm. will have what 
volume at 50° C. and 760 mm.? 

462. Quantity of Heat. The thermometer alone does not 
measure quantity of heat. It measures temperatures. If 
10 kilograms of water is held in a reservoir so that it can 
fall 10 meters over a wheel, it has 100 kilogram-meters of 
potential energy. One kilogram of water at the same height 
would have but one-tenth as much energy. So to raise 
the temperature of 10 kg. of water 10° takes 10 times as 
much energy as to raise 1 kg. the same number of degrees. 
A barrel of warm water contains far more heat than a teacup- 
ful of boiling water. 

463. Heat Units. The quantity of heat required to raise 
one gram of water one Centigrade degree is the unit of heat 
called the calorie. This quantity is not precisely the same 
for water at different temperatures, but the differences are 
small enough to be considered only in work of the highest 
accuracy. Another unit which is sometimes employed is 
the amount of heat required to raise 1 pound of water one 
Fahrenheit degree. Engineers call this unit the B. T. U. 
(British Thermal Unit). 

464. Specific Heat. Other substances than water (except- 
ing hydrogen) require less than one calorie to raise the tem- 
perature of one gram one Centigrade degree. The specific 
heat of any substance is an abstract number. For nearly 
all substances this number is less than 1 and is expressed as 
a decimal fraction. It is most conveniently described by 
saying that the specific heat of a substance is the fraction of 
a calorie required to raise the temperature of 1 gram of it 1 
degree Centigrade. To be more accurate we should say 
that it is the ratio of this quantity of heat to one calorie, 
the quantity which raises 1 gram of water 1° C. This ratio 
would be the same for any other mass, of course. Thus the 
number of calories which raise the temperature of 200 grams 
of the substance 1° C, divided by 200 calories will give the 
same number. 



230 HEAT 

Table of Specific Heats at 20° C. 

Aluminum 214 Platinum 032 

Copper . . ' 092 Silver 055 

Iron 109 Tin 054 

Lead 030 Zinc . 092 

Mercury 033 Glass (crown) 161 

Alcohol 600 Brass 090 

Air . . . . . . . .238 Paraffin 694 

Hydrogen . . . . .3.406 Ice (at 0°) 501 

465. Determination of Specific Heat. If equal weights of 
water at 0° and mercury at 100° were mixed and no heat 
escaped or was added from outside, the temperature of the 
mixture would be about 3.2°. The specific heat of the mer- 
cury is about -g 1 ^- that of water. The heat which raises 
the temperature of the water comes from an equal mass of 
mercury. The mercury must fall 30 times as much in 
temperature as the water rises. 

466. To determine the specific heat of a substance, several 
methods are employed, but the method of mixtures is the 
most simple and direct. Suppose 400 grams of lead shot at 
100° C. mixed with 200 grams of water at 18°, and that the 
temperature of the mixture is found to be 22.4°; the specific 
heat of the lead may be calculated. The water should be 
contained in a thin, polished metal vessel. This vessel will 
also have been raised 4.4° in temperature. Let its weight 
be 100 grams and its specific heat .1. To raise its tem- 
perature 1° would take 10 calories. The water equivalent 
of the vessel is 10. That is, it takes as much heat to raise 
the vessel 1° as to raise 10 grams of water 1°. To raise 
the vessel 4.4 degrees takes 44 calories. 1 

The 200 grams of water rose 4.4°, taking 880 calories. The 
sum of these two amounts of heat, 924 calories, was given out 
by 400 grams of lead. One gram gave out ffo X 924 = 2.31 
calories in falling 77°. In falling one degree, one gram gave 

1 This quantity is such a small part of the total heat involved, that a 
fairly good approximate result may be obtained if we neglect it. 



MECHANICAL EQUIVALENT OF HEAT 



231 



W 



out T y X 2.31 = .03 calorie. Therefore, .03 calorie would 
heat 1 gram of lead one degree, and the specific heat of lead 
is .03. 

467. Mechanical Equivalent of Heat. Joule determined the 
number of foot-pounds of work necessary to raise the tem- 
perature of one pound of 
water 1 Fahrenheit degree. 
He arranged his apparatus 
essentially as shown in the 
diagram. A weighed quan- 
tity of water was placed in 
the vessel C (called a calori- 
meter). A paddle wheel with 
vanes V revolved in the cal- 
orimeter. Stationary vanes 
S prevented the water from 
whirling around. Weights W 
caused the paddle-wheel to 
turn. A thermometer T in- 
dicated the temperature. 
Precautions were taken to 

prevent heat from being communicated to or from the 
vessel C, and to avoid friction of the bearings. 

468. The product of the weights W by the distance 
through which they fell gave the amount of work done, and 
the weight of water in C multiplied by the number of degrees 
through which its temperature rose gave the number of 
heat units generated. The quotient of the number of units 
of work divided by the number of units of heat was 772. 
Joule concluded that 772 foot-pounds are equivalent to one 
heat-unit, or that 772 foot-pounds of work will heat one 
pound of water 1° Fahrenheit. Some corrections which 
Joule omitted raise this value to 776 foot-pounds. Reducing 
this to metric units, we have 426 gram-meters per calorie. 
One gram-meter is equivalent to 980 X 100 ergs. We have 
then, 1 calorie = 426 X 98,000 ergs = nearly 42,000,000. 
This is often written 4.2 X 10 7 . 






J0s 

5 c 


w ff 


8 


r J 



Fig. 259 



232 HEAT 

Many other methods have been used, and many investi- 
gators have worked at the problem. A mean of all the best 
results is very nearly 4.2 X 10 7 ergs per calorie. 



PROBLEMS. 

1. One pound — 453.6 grams. How many calories are 
there in one British thermal unit ? 

2. 200 grams of stone at 98° C. were placed in 200 grams 
of water at 13° C, contained in a brass calorimeter weighing 
90 grams. The temperature rose to 28° C. Find the specific 
heat of the stone. 

3. Niagara Fall is 160 feet high. Determine the differ- 
ence of temperature at top and bottom as a fraction of a 
Fahrenheit degree. 

4. How many ergs are required to raise the temperature 
of 1 kilogram of alcohol one Centigrade degree ? 

5. 500 g. of iron filings at 99° C. were mixed with 200 g. 
of water at 11° C. in the calorimeter of Ex. 2. The temper- 
ature of the mixture was 29° C. Compute the specific 
heat of iron. 

CHANGE OF STATE. 

469. All elementary substances and many others are 
capable of existing in all three physical states: solid, liquid, 
and gaseous. Water is an example of a substance whose 
three forms are familiar to every one. The difference be- 
tween ice and water is, in general, simply a difference in the 
quantity of heat-energy present. The same is true for water 
and steam. 

470. Fusion. If a piece of ice at —10° C. be brought into 
a warm room, its temperature rises and presently it begins 
to melt. This process of conversion into a liquid by heat 
is called fusion (Latin fusus, poured). While the ice is 
melting it continues to receive heat without rise of tem- 
perature. 



MEASUREMENT OF LATENT HEAT 233 

471. Melting Point. Freezing Point. In the case of water 
the change from solid to liquid or from liquid to solid takes 
place at the same sharply defined temperature, 0° C. This 
is called either the melting point of ice or the freezing point 
of water. Some other substances have pretty sharply 
defined melting points, and are perfectly solid until this 
point is reached and then become definitely liquid. A 
number of metals, including zinc, lead, and tin, are so. Glass, 
on the contrary, gradually softens and passes into a liquid 
by insensible degrees. Butter, beeswax, and many familiar 
substances behave in this way, and are said to have vitreous 
fusion. 

472. Latent Heat of Fusion. The heat received by the ice 
while melting is called latent heat, which means hidden heat, 
because it does not raise the temperature. The amount 
of heat required to melt 1 gram of ice is nearly 80 calories. 
The latent heat of fusion of ice is 80 calories. In other 
words, it takes 80 times as much heat to melt ice as to raise 
the temperature of the same amount of water 1 ° C. This heat 
is the energy required to pull the molecules of the ice apart. 
It is present in the water, and we may imagine it occupied 
in keeping the molecules of the water separated. It is 
probably nearly all kinetic energy of the molecules of the 
water. The usefulness of ice as a refrigerant is due to the 
great quantity of heat necessary to melt it. It absorbs 
heat from warm bodies as a towel or sponge absorbs water 
from damp ones. The analogy is very imperfect, since the 
towel becomes damp with use, but the ice absorbs heat and 
stays cold. 

473. Measurement of Latent Heat of Fusion of Ice may be 
well made by the method of mixtures. Suppose 202 grams 
of water at 35° C. in the calorimeter described in paragraph 
466, and that 75 grams of ice having been melted in it the 
temperature fell to 5° C. Now the water and calorimeter 
gave out (202 + 10) X 30 = 6360 calories in cooling from 
35° to 5°. Of this heat 375 calories were used in raising 
to 5° the 75 grams of water resulting from the melted ice. 



234 



HEAT 




Fig. 260 



The remainder, 5985 calories, melted the ice. It took, 
therefore, 5985 -r- 75 = 79.75 calories to melt one gram of 
ice. 

474. Temperature of Greatest Density for Water. If a 
quantity of water at 40° C. be cooled, it will contract in 
volume until it reaches 4° C, when it will 
cease to contract, and if cooled further will 
expand. This may be proved by means of a 
vessel such as that shown in Fig. 260. A 
ring-shaped trough surrounds the vessel, and 
this is filled with salt and ice. The vessel 
is filled with water at 10°. For a time the 
lower thermometer indicates a lower tem- 
perature than the upper, but when the lower 
has reached 4° C, the upper continues to fall 
to 0°, showing that water is denser at 4° 
than at lower temperatures. 

This is a fact of great importance, since it 
prevents bodies of water from freezing solid. Ponds cool off 
at the top by contact with the air and by radiation (paragraph 
512). The surface water, cooling, sinks and is replaced by 
warmer water from below, until the temperature of the whole 
pond has fallen to 4° C. After that the surface water cools to 
0°, remains on top, and freezes, while the lower part remains 
at 4° C, the temperature of greatest density for water. Most 
liquids continue to contract with fall of temperature. 

475. Water Expands in Freezing. During the process of 
freezing, water expands about -^ of its volume, so that ice 
floats with about -^ of its volume above water. If a bottle 
be filled with water and tightly corked and immersed in 
in a freezing mixture or put out of doors on a very cold night, 
the bottle will be burst. Even iron vessels are sometimes 
broken in this manner, and the bursting of water-pipes in 
cold weather is a painfully familiar fact to householders 
in many parts of our country. 

476. Effect of Pressure on Freezing Point. Since ice occupies 
more space than water, it is clear that pressure will tend to 



FREEZING MIXTURE 



235 



prevent water from freezing, and therefore water under 
pressure will freeze at a temperature lower than 0° C. Each 
added atmosphere of pressure lowers the freezing point about 
.0072 of one degree Centigrade. On the other hand, sub- 
stances like paraffin which contract on solidifying have 
their melting points raised by pressure. 

477. Regelation. If two pieces of ice at 0° C. be pressed 
together, a little ice melts at the points of contact, taking 
the heat necessary to melt it from the surrounding ice. 
When the pressure is relieved, the water being surrounded 
by ice a little below the freezing point, it freezes, and the 
two pieces of ice are found frozen together. This phenome- 
non is called regelation, and is supposed to account for the 
motion of glaciers. When a boy crushes together a handful 
of damp snow, the crystals melt at the points of contact and 
freeze together, making a hard ball. Skates glide over 
ice easily because the film of water melted by pressure 
acts as a lubricant. Skating at very low temperatures 
is impossible because the ice does not melt under the skates. 

478. A simple and very striking 
experiment in regelation is shown 
in Fig. 261. A piece of ice not 
more than 7 cm. square is supported 
on blocks of wood. (Two chairs 
placed side by side do very well.) 
A slender wire (about No. 24) is 
passed around the ice, and a weight 
of 10 kilograms hung on it. The 
wire is gradually forced through the 
ice, the water flowing past the wire 

and freezing above it. When the wire has passed entirely 
through, the ice is found frozen together as firmly as before. 

479. Freezing Mixture. If a vessel of cream be packed 
in cracked ice, in warm weather, it may be cooled to 0° C, 
but will not freeze. If, however, salt be mixed with the ice, 
the cream may be frozen. The tendency of salt to dissolve 
in water is so strong that the salt takes water from the ice, 



□ 



Fig. 261 



236 HEAT 

that is, causes it to melt. In order to melt, the ice must 
absorb heat and render it latent. This heat is partly ob- 
tained from adjoining objects, but a part of it is the sensible 
heat of the ice itself. The result is a solution of salt at a 
temperature below 0° C, sometimes as low as 0° F. The 
heat of the cream passes through the can into this cold brine. 
When the temperature has fallen to the freezing point of 
the cream it begins to give up its latent heat, and so to freeze. 
A liquid cannot freeze unless it can give heat to another body 
whose temperature is below its own freezing point. 

480. Heat of Solution. Sometimes when solids dissolve 
in liquids the temperature rises in consequence of chemical 
action. This is the case when caustic soda or potash dissolves 
in water. In other cases, the temperature falls, as we should 
expect, since heat is required to convert a solid into a liquid. 
If a handful of ammonium chloride, or the substance which 
photographers call "hypo," be dissolved in a glass of water, 
a considerable fall of temperature may be observed. 

481. Solution of Liquids in Gases and of Gases in Liquids 
may be studied by observing the behavior of water and air 
toward each other. Air dissolves more freely in cold water 
than in warm. If a glass of cold water be allowed to stand 
until it becomes warm, many bubbles of air separate out from 
the water and settle on the glass. If water be boiled, the 
air is entirely expelled. Water drawn from a hot-water 
faucet in winter is often full of fine bubbles of air, giving 
it a milky appearance. The air has been driven out of solu- 
tion in the heating process, and has had no opportunity 
to escape. 1 

482. Water dissolves in air even when it is cold, and 
much more freely at higher temperatures. The process 
seems to be the same, whether air is dissolving in water or 
water in air. The rapid motion of the molecules carries 
some of them across the bounding surface between the air 

1 If the pressure in the pipes is high, the air will be retained in solution 
until the pressure is released by the escape of the hot water from the pipe 



DEW-POINT— PRECIPITATION 237 

and water. Some of the molecules of water near the top 
move upward with sufficient velocity to carry them through 
the surface film into the air. When the temperature is 
higher, the average molecular velocity of the water is greater, 
and the number of escaping molecules is larger. In any 
case, when the molecules have escaped from the water they 
remain in the air and assume the gaseous condition, so to 
speak. 

483. Some of the molecules of air near the surface of the 
water, darting about like tiny projectiles, are continually 
penetrating the surface film and passing into solution in the 
water. Molecules of water vapor from the air also pass into 
the water, and when the rate at which this is going on just 
equals the rate at which the water is escaping into the air, 
the air is said to be saturated with vapor. 

484. Effect of Temperature on Evaporation. The process of 
passing from liquid into vapor is called evaporation. Many 
other liquids besides water evaporate. Such liquids are said 
to be volatile (Latin volare = to fly). Alcohol and ether 
are far more volatile than water, glycerin and olive oil less 
so. For liquids in general, the higher the temperature the 
more rapid the evaporation; that is to say, the quantity of 
vapor necessary to saturate a gas increases with rise of 
temperature. 

485. Dew-point. Precipitation. If air be cooled indefi- 
nitely, a temperature will be reached at which the quantity 
of water vapor present will be sufficient to saturate it. When 
it is further cooled, some of the vapor begins to condense 
into water particles which remain suspended 1 in the air, 
forming mist. If the quantity condensed is large, the par- 
ticles of mist unite to form rain drops. The temperature 
at which air containing a certain percentage of moisture 
becomes saturated is called its dew-point, and the separation 
of mist from the air is called precipitation. The dew-point 
may be determined in warm weather by stirring bits of ice 

1 See paragraph 94, etc., for explanation of suspension. 



238 HEAT 

in water contained in a polished metal vessel, and noting the 
temperature at which tiny drops of water begin to form 
on the vessel. From the dew-point, by the aid of tables, 
we may determine the percentage of moisture in the air. 

486. The Formation of Clouds is well illustrated by a simple 
experiment with the air-pump. Place a moistened sponge 
or piece of cloth on the plate of the air-pump. Fit to the 
plate a bell- jar which should be large enough to contain a 
thermometer. After the apparatus has stood a few minutes 
the air in the vessel will be nearly saturated by evaporation 
from the sponge. Now make not more than two quick 
strokes of the pump. The column of mercury in the ther- 
mometer will fall slightly, and a cloud will form in the jar. 
On re-admitting the air, the cloud will quickly dissolve. 

487. This experiment illustrates almost perfectly the way 
in which clouds are often formed in nature. When the 
piston is lifted, the air in the jar expands slightly, and in so 
doing does work, which uses up some of its heat energy, and 
so it becomes cooler. The cooling of the saturated air 
decreases its capacity for moisture, and precipitation takes 
place. When the air is again admitted, the pressure of the 
atmosphere compresses the air in the jar, and in doing work 
on it raises its temperature, thus increasing its capacity for 
moisture and causing the cloud to be redissolved. When 
the southeast trade-winds climb the slope of Table Mountain, 
South Africa, they rise to regions where the pressure of the 
atmosphere is less, expand in consequence of diminished 
pressure, do work in expanding against the reduced pressure, 
are cooled by using up their heat to do work, and the moisture 
is condensed in consequence of the cooling. Thus is formed 
the cloud cap that hangs during several months of each year 
on the top of Table Mountain. As the air flows down the 
western side, it is warmed by descending into a region of 
greater pressure, its capacity for moisture is increased, and 
the cloud melts away. 

488. On a sunny day in summer many beautiful white, 
fleecy clouds are often seen. They have nearly level lower 



VAPOR PRESSURE 239 

surfaces, at a height above the earth which is the same 
for all the clouds visible at a given time. This is the height 
at which the air becomes cold enough to reach its dew- 
point. On some days such clouds are not seen because there 
is not enough moisture to form them. In arid regions these 
"cumulus" clouds almost never occur. 

489. Effect of Evaporation on Temperature. When we wish 
clothes to dry, we hang them where there is a breeze, if 
possible, so that fresh unsaturated air may come in contact 
with them. The object which is being dried often falls very 
much in temperature, having furnished a part of the heat 
to evaporate the water. In warm dry countries, such as the 
southern point of Nevada, water is cooled by hanging an 
unglazed jar of it in the shade and swinging it back and 
forth. The water soaks through the porous jar, forming 
a thin film of water on the outside, which in the dry atmos- 
phere evaporates very rapidly. The temperature of the 
bodies of warm-blooded animals is kept from rising above 
normal by increased evaporation from the surface in hot 
weather. In a dry atmosphere heat is much less oppressive 
than when the air is nearly saturated, so that evaporation 
is slow. Such weather we call sultry, and we say that the 
humidity is high. 

490. Boiling, or, as it is sometimes called, ebullition, is 
simply the act of passing off in vapor violently instead of 
quietly. Bubbles of vapor form in the liquid, rise to the 
surface, and burst. At a given pressure, this always takes 
place at the same temperature for a given liquid. If a 
vessel of water is being heated at the bottom, bubbles of 
steam form at the bottom a little while before the water 
actually boils. These tiny bubbles rise a short distance and, 
condensing in the cooler water above, collapse, causing the 
simmering noise heard just before water boils. At 100° C. and 
standard atmospheric pressure, steam occupies about 1700 
times as much volume as the water from which it was formed. 

491. Vapor Pressure. Suppose a drop of water released 
under the open end of a barometer tube. It would rise to 



240 



HEAT 



A 



19 
-78 
77- 
76- 

75- 



n 



m 



74Hy 



Fig. 262 



the vacant space at the top and, if the space were large 

enough, completely evaporate. The mercury column would 

fall a little, because the water vapor exerts 

a pressure on it, partly counterbalancing 

the pressure of the atmosphere which is 

holding the mercury. If a number of drops 

of water were admitted, not all of it would 

evaporate, the remainder lying on top of 

the mercury. In Fig. 262, A represents 

the upper part of a barometer tube, B 

showing the condition when a few drops 

of water have been admitted, the residue 

of the water lying at W. The distance 

through which the column falls, due to the 

vapor pressure (or tension) of the water, increases with the 

temperature. It is about 1.7 cm. at 20° C. At the same 

temperature the vapor pressure of alcohol is 4.4 cm., and 

that of carbon disulphide is nearly 30 cm. 

492. Effect of Pressure on Boiling Point. The boiling point 
of a liquid is simply the temperature at which its vapor 
pressure equals the pressure of the atmosphere. It is clear 
that if the pressure on the liquid be increased, the boiling 
point must rise, because the vapor pressure must increase 
to equal the greater pressure, and this increase of vapor 
pressure means rise of temperature. Of course, diminished 
pressure lowers the boiling point. The statement that 
water boils at 100° C. implies that the pressure on it is one 
atmosphere, equivalent to 760 mm. of mercury. On top 
of Pike's Peak the temperature at which water boils is too 
low to cook potatoes, so that they must be fried or roasted. 
In the process of canning corn it must be heated above 100° 
C. This is done by immersing the cans in water in a steel 
tank, fastening a lid on and boiling them under pressure. 
In a locomotive boiler the temperature is sometimes as high 
as 190° C. 

493. The effect of diminished pressure is well illustrated 
by the experiment shown in Fig. 263. A round-bottomed 



DETERMINATION OF BOILING POINT 



241 



flask is half filled with water and the water boiled over a 

Bunsen burner or alcohol lamp. When the steam flows 

freely from the neck, the flask is corked and the flame 

removed at the same 

moment. The flask 

is then inverted and 

supported over a 

vessel of cold water. 

The upper part of 

the flask, apparently 

empty, is now full 

of vapor of water, 

which at the boiling 

temperature we call 

steam. So long as 

the temperature of 

the vapor is the same 

as that of the water, 

nothing happens, but 

when a little cold 

water is poured on 

the flask, the vapor is 

cooled, causing it to 

contract and exert less pressure on the water. Under this 

diminished pressure the water again boils. By continuing to 

pour cold water on the upturned flask, the water may be 

made to go on boiling until its temperature is so reduced 

that it feels cool to the hand. 

494. Determination of Boiling Point. In determining the 
boiling point of a liquid, the thermometer should be immersed 
in the vapor, not in the liquid. The temperature of the liquid 
is higher as the distance from its surface increases, because 
its boiling point is raised by the pressure of the liquid 
itself. Another reason for the precaution is that dissolved 
solids in the liquid raise its boiling point and dissolved 
gases lower it, but neither of these things affects the tem- 
perature of the vapor. 
16 




242 



HEAT 



495. Distillation. In order to free liquids from dissolved 
solids they are boiled, and the vapor condensed. This 
process is called distillation. Ocean-going vessels carry 
stills j so that if their supply of fresh water gives out they 
may distil salt water. Whiskey is distilled from a "mash" 
of fermented grain, and brandy from fermented fruit juice. 




Fig. 264.— Still. 



Alcohol being more volatile than water, these liquors have 
a higher percentage of alcohol than those prepared from 
similar materials by fermentation only. The liquid to be 
distilled is boiled in the vessel a. The vapor is condensed 
by passing through the "worm" d, immersed in a vessel of 
cold water, and comes out in liquid form at the end of the 
spiral tube. 

496. The Latent Heat of Vaporization of Water is about 
537 units. One method of measuring it is exactly analogous 
to that already described for latent heat of melting ice. 
A weighed quantity of cold water is placed in the can C 
(Fig. 265). Steam from any convenient supply enters the 
trap B by the pipe S. Water which condenses in the pipe 
S is caught in the trap, and dry steam passes through the 
tube D into the water, whose temperature has been noted 



LIQUEFACTION OF GASES 



243 




Fig. 265 



just before the steam was admitted. When the temperature 
has risen as much above the temperature of the room as 
it was below at the start, the can is taken away from the 
steam supply. The temperature of the water is observed, 
and the can and water again weighed to 
determine the quantity of steam condensed. 
Suppose 351 grams of water at 5° C. in the 
calorimeter of paragraph 466, raised to 35° 
by the condensation of 18 grams of steam. 
The number of calories used in heating water 
andean would be (351 + 10) X 30 = 10830. 
Of this quantity 18 X 65 calories were con- 
tributed by the water from the condensed 
steam in cooling from 100° to 35°, leaving 
10830 — 1170 = 9660 calories due to the con- 
densation of 18 grams of steam. This gives 
for the latent heat given out by one gram in 
condensing, 9660 -t- 18 = 537, nearly. This 
amount of heat must be the same as that 
taken up by one gram of water in evaporating, so we may 
say that the latent heat of steam is 537 units, or that it 
takes 537 times as much heat to evaporate water as to raise 
the same amount of water one Centigrade degree. 

497. This vast amount of heat contained in D A 
steam accounts for the length of time required 
to boil water away. If a vessel of water at 
22° C. placed on the stove rises 3 Centigrade 
degrees per minute, it will take about 26 
minutes to begin to boil, and about three 
hours to boil away, supposing the heat supply 
constant. 

498. Liquefaction of Gases. Many gases, in- 
cluding ammonia, carbon dioxide, and chlor- 
ine, may be liquefied at ordinary temperatures 
by compressing them. For each gas, however, 
there is a temperature above which no press- 
ure, however great, will reduce the gas to a Fig. 266 



M 



244 HEAT 

liquid. Carbon dioxide at 31° C. becomes, under a pressure 
of 77 atmospheres, a clear, colorless liquid. At lower tem- 
peratures, the necessary pressure is less. Fig. 266, A, shows 
a strong glass tube half filled with this liquid and sealed, as 
it would appear at any temperature below 31° C. If the 
temperature be slowly raised, the meniscus M, showing the 
surface of the liquid, disappears at 31°, and the whole tube 
is soon filled with an invisible gas. 

If a quantity of liquid carbon dioxide be allowed to escape 
into the air, the rapid evaporation takes up so much heat as to 
cause a part of the liquid to freeze. 

499. The critical temperature of carbon dioxide is 31°, 
of ammonia 130°, and of chlorine 141° C. Such gases as 
oxygen, hydrogen, and nitrogen, whose critical temperatures 
are very low, were formerly called permanent gases, because 
they cannot be liquefied at ordinary temperatures. In the 
method first employed in liquefying these gases, one of the 
first steps is to make a freezing mixture of hydrochloric acid 
and solid carbon dioxide, which gives a temperature of 
■ — 77° C. This suffices to liquefy ethylene gas, and by the 
rapid evaporation of liquid ethylene a temperature of 
— 150° C. may be obtained. This is low enough to liquefy 
both nitrogen and oxygen under heavy pressure. When 
the pressure on such a liquid is released, a part of it evapo- 
rates, and in so doing cools the remainder to a temperature 
so low that it can remain liquid under a pressure of one 
atmosphere. For oxygen and nitrogen these temperatures 
are — 183° and — 194° C. respectively. In other words, the 
boiling point of oxygen is — 183° C. and of nitrogen — 194°. 

500. Cooling by Expansion. When an engine is driven 
by compressed air, the escaping air is very cold, because of 
the work which it has done in expanding. This fact is made 
use of in the machines now used to produce liquid air. 
Highly compressed air is cooled and allowed to expand. 
In so doing it cools to a very low temperature a fresh quantity 
of still more highly compressed air. By the rapid expansion 
of this, a temperature below — 150° is produced, and a third 



ICE MACHINES 



245 



quantity of compressed air is liquefied. When the solid 
carbon dioxide has been filtered out of it, liquid air is a clear 
liquid with a very pale blue tint. At atmospheric pressure, 
if protected from heat, it boils slowly, the nitrogen, whose 
boiling point is lower, escaping first. Nearly pure oxygen 
is obtained in this way for medical uses. Liquid air has 
much the same effect on the skin as red-hot iron, producing 
painful burns which heal very slowly. The skin suffers 
as much from having its molecular motion so nearly stopped 
by liquid air as by having it very much increased by contact 
with hot iron. One would be just as much hurt by running 
at the rate of 10 miles an hour against a brick wall as by 
being struck by the flat end of a freight car moving 10 miles 
an hour. 

501. Ice Machines. The usual method of making arti- 
ficial ice involves the use of liquefied ammonia gas. 1 The 
ammonia is sent through 
pipes A, immersed in brine 
in a tank. The evaporation 
of the ammonia takes heat 
from the brine and lowers 
its temperature to about 
—10° C. Metal vessels T, 
filled with water, are partly 
immersed in the brine, and 
the water is thus frozen. 
The ammonia passes after 
evaporation to a com- 
pressor which again reduces 
it to a liquid. This is cooled by passing through coils im- 
mersed in cold water, and returned to the pipes A to be again 
evaporated. 

Another method of ice manufacture now coming into use 
employs the expansion of compressed air instead of ammonia. 




Fig. 267. 



-Ammonia ice-making 
process. 



1 This must not be confused with ordinary "ammonia," which is a 
solution of ammonia gas in water. 



246 HEAT 

EXERCISES AND PROBLEMS. 

1. If one's hand is thoroughly wet and held in a current 
of warm air, it feels cold. Why is this? 

2. In the measurement of latent heat of steam, why do 
we choose the range of temperature from 15° below the 
temperature of the room to 15° above? 

3. Why does a pail of water in a fire-proof safe tend to 
prevent the contents of the safe from being scorched? 

4. Why does the housewife sometimes place a vessel of 
water in the oven when she is baking cakes? 

5. A tub of water in a small conservatory will sometimes 
prevent plants from freezing in severe weather. Why? 

6. A hand wet with alcohol feels much colder than one 
wet with water. Why? 

7. In the experiment of paragraph 493, why is not a flat- 
bottomed flask as satisfactory as a round-bottomed one? 
Why must the flame be removed when the cork is put in ? 

8. What is the difference between clouds and fog? 

9. Why cannot snow-balls be made from cold snow? 

10. How much steam at 100° C. would be required to 
melt 100 kg. of snow at 0° C? 

11. Why would a thick wire be less satisfactory for the 
experiment of paragraph 478? 

12. 20 grams of ice at 0° C. is stirred into 100 grams of 
water at 30° C. Disregarding the heat capacity of the con- 
taining vessel, what would be the temperature of the mixture ? 

13. How much steam at 100° C. must be passed into a 
metric ton of water at 8° C. to raise its temperature to 60° 
C. ? Disregard the heat capacity of the vessel. 

DISTRIBUTION OF HEAT. 

502. We always associate heat with some substance, and 
it is a matter of common observation that hotter objects 
give heat to cooler ones which are near them, or in some 
instances at a distance. They do this in several ways: by 
conduction, convection, and radiation. 



MEASUREMENT OF CONDUCTIVITY 247 

503. Conduction. If we take hold of a heavy metal bar 
which is warmer than the hand, heat flows from the metal 
to the hand. The part which we have grasped does not at 
once become appreciably cooler than the rest, because heat 
flows from other parts to replace that which has been taken 
away. If one end of a short copper rod be put in the fire, the 
whole rod quickly becomes hot. This flow of heat through 
a substance is called conduction. When one end of a rod 
is heated, the molecules there are set into more rapid motion 
than before and so disturb those next to them. The energy 
is thus passed on from molecule to molecule throughout the 
bar. 

504. Metals are Good Conductors. Substances differ in 
their ability to conduct heat. Silver is the best con- 
ductor, and copper but little inferior. All metals are good 
conductors compared with other things, but they differ 
much among themselves. If a cylinder of wood and one of 
metal (preferably brass) of the same diameter be placed 
end to end and one thickness of writing paper wrapped 
neatly around both, the edges of the paper overlapping, 
and pasted fast, and the covered cylinder be held in a 
flame, the paper will be charred where it rests upon wood, 
but not where it rests upon metal. This is because the 
heat which passes through the paper is quickly carried away 
from the surface by the conducting brass, but not by the 
non-conducting wood. One of the 
best solid non-conductors is wool. 
This property of wool explains its 
use as a material for winter clothing. 

505. Measurement of Conductivity. 
The conductivity of different metals 
may be roughly compared by the 
apparatus shown in Fig. 268. The 
metal vessel has several rods inserted Fig. 268.— Conductometer. 
in brass sockets attached to one side. 

The rods are of the same size but of different metals. A marble 
is fastened to each by paraffin. Hot water being placed in 




248 HEAT 

the vessel, the marbles drop off in succession. The difference 
in the time at which the paraffin melts and releases the 
marble is not wholly due to difference in conductivity. It 
depends on other things also, chiefly the specific heat of the 
metal. A rod which is a good conductor and has high 
specific heat may hold its marble longer than one which is 
a poorer conductor and has much lower specific heat. Ac- 
curate measurements of heat conductivity are difficult. 

Heat Conductivity at 15° C. (Compared with Silver =1.) 

Silver . . 1.00 Iron . . .15 Marble . . .0050 

Copper . . .95 Zinc . . .27 Glass . . .0023 

Aluminum . .31 Platinum . .06 Cork . . .0006 

Brass. . . .28 Paper . . .0001 Wool . . .0001 

506. Liquids are Poor Conductors. If a piece of ice be put 
into a test-tube and held down by a piece of metal, and the 
tube then filled with cold water, the water in the upper 
part of the tube may be boiled without melting the ice. 
A still mountain lake may be warm on the surface in mid- 
summer and quite cold at a depth of ten feet, because water 
is such a poor conductor. Most liquids conduct heat very 
slightly. 

507. Gases do not Conduct Heat nearly so well as liquids 
or solids. They were long supposed to be perfectly non- 
conducting. Air spaces in house walls help to keep the house 
warm in winter and cool in summer. Several layers of thin 
clothing keep one warm better than one heavy layer weighing 
as much as the several thin ones. This is because of the 
layers of air included between the thicknesses. 

508. Convection is from the same root as the verb convey. 
When a heated substance moves, it conveys heat. The 
substance may be called the vehicle, just as the druggist 
uses water and other liquids as vehicles for medicines. 
Air that is heated in the cellar and carried by flues to the 
rooms of the house heats the house by convection. The air 
rises because, it has been expanded by heat, and so become 
less dense than the surrounding air, which forces it up. 



RADIATION 



249 



O 



509. Hot-water Heating. A simple case of convection is 
that of a vessel of water heated from the bottom. The heated 
water expands, and rises because of diminished density, 
thus causing a circulation which 
distributes the heat throughout 
the vessel. The "circulating 
boiler" for furnishing hot water 
in houses works in the same 
way. Water from a reservoir at 
a height flows into the boiler by 
the inlet I, whenever any faucet 
connected with the outlet is open. 
This entering water is delivered 
at the bottom, and being cold 
does not mix rapidly with the 
warmer water above, but in rising 
forces it out at the outlet 0. 
The pipe AWB forms a circu- 
lating system when heated at W. 
W (sometimes called a 




Fig. 269. — Circulating boiler. 



This is done by putting 
water-back") in the firebox of the 
stove. The direction of circulation is indicated by the arrows. 
On flowing back into the boiler at B, the hot water tends to 
rise to the outlet. 

510. The same kind of circulating system is used for 
heating greenhouses and other buildings. It is only necessary 
to make the pipe AWB long enough to reach from the fire 
to the farthest room to be heated, and to insert coils of pipe, 
called radiators, at intermediate points where heat is wanted. 

511. Steam Heating. The large amount of heat latent in 
steam makes it a very efficient agent for heating buildings, 
since all the heat used in evaporating the water is given out 
again when the steam is condensed. The steam is conveyed 
from the boiler to the place where the heat is needed, not by 
its own tendency to rise, but by the pressure of other steam 
behind it. 

512. Radiation. When a hot object is suspended in the 
air, it loses heat by convection currents in the air. That 



250 HEAT 

its heat energy is not given off through these currents alone 
is shown by the fact that one gets the sensation of heat by 
holding his hand below the object or at one side of it. The 
mode by which objects are heated at a distance from the 
source without any material agency between object and 
source is called radiation. The moving molecules of the hot 
body act upon the ether and set up vibrations in it. The 
train of ether waves carries away the energy of the body, 
and when these waves strike upon another body, they may 
in turn set its molecules into vibration, and so heat it. 

513. Ether waves of all lengths, including light, heat, and 
many which are neither light waves nor heat waves, are 
called collectively radiation, and the term solar radiation 
includes all the energy which we receive from the sun. It is 
estimated that the whole amount of solar radiation received by 
the earth in a year would be sufficient to melt a layer of ice 
covering the entire earth to a depth of more than 100 feet. 

514. Radiation Absorbed, Reflected, or Transmitted. When 
solar radiation falls upon a dark, rough surface, such as 
plowed ground, a large proportion of it is absorbed, and 
heats the body absorbing it. Smooth, light-colored surfaces 
reflect a large part of the radiation which falls upon them. 
All reflection of radiation follows the same laws as reflection 
of light. Certain substances such as air and glass transmit 
without interruption trains of waves which fall upon them 
in the same manner that they transmit the particular wave- 
lengths which we call light. Such substances are called 
media (singular = medium). 

515. Good Absorbers are Good Radiators. Dark-colored 
objects in general are good absorbers, particularly if the 
surface be rough. The character of the surface has much 
to do with the proportion of the incident radiation which is 
absorbed or reflected. If a bright metallic surface be coated 
with carbon, its absorbing power is much increased, and of 
course its reflecting power to the same extent decreased. 
This is shown by taking two similar bright cans, smoking 
one of them in a kerosene or turpentine flame, filling them 



GREENHOUSES 251 

with cold water at the same temperature, and placing them 
in the sunshine. The water in the blackened can will rise 
in temperature more rapidly. If the same two cans be filled 
with hot water at the same temperature and placed in a 
cool room, the black one will cool more rapidly. Polished 
metallic surfaces are the best reflectors as is the case with 
light. The experiment just described shows that good 
reflectors are poor radiators. 

516. Selective Absorption. All substances absorb some of 
the radiation which falls upon them. Air absorbs but little 
of the solar radiation, transmitting nearly all. The atmos- 
phere is therefore heated but little by the direct rays of the 
sun. The earth, on the contrary, absorbs nearly all the solar 
radiation and is heated by it. The earth and other bodies 
of low temperature give out radiation whose wave-lengths 
are very much greater than those of waves from very hot 
bodies such as the sun. These long waves sent out by the 
earth are absorbed by the atmosphere near the earth's 
surface, and thus the air derives its heat chiefly from the 
earth's radiation. Selective absorption is shown by all 
bodies which transmit radiation. Glass absorbs the long 
waves in the same manner as air, but to a much greater 
extent. A pane of glass which transmits sunshine almost 
without being heated at all will absorb or reflect nearly all 
of the radiation from a black stove, transmitting almost 
none. The amount of absorption by any medium depends 
on the distance which the radiation travels through the 
medium. 

517. Greenhouses. When the sun shines it is warmer in 
a greenhouse even without a fire, than it is out of doors. 
This is because the glass of the greenhouse behaves some- 
what like the atmosphere, permitting the short waves of the 
solar radiation to pass through, but reflecting or absorbing 
the long waves which are sent back by the objects inside 
the greenhouse. Someone has combined scientific truth 
and poetic fancy in calling a greenhouse "a trap to catch 
sunbeams.'! 



252 HEAT 

518. Relation between Wave-length and Amplitude. So 

far as we know, there is no definite and necessary relation 
between the amplitude of ether vibrations and their wave- 
length, but it is true in general that the hotter a body is 
the greater is the amplitude of the ether waves which it 
sends out, and the shorter their average wave-length. The 
temperature of a body has to do with the amount of energy 
a body gives out, the total energy being dependent on the 
amplitude of the vibrations, and their complexity increasing 
with the amplitude. This is analogous to the sound 
waves due to a vibrating plate. A plate which is struck 
very gently gives an almost pure fundamental note of small 
amplitude. When it is more strongly excited, overtones 
are added, often entirely masking the fundamental. 



HEAT ENGINES. 

519. Heat the General Source of Mechanical Energy. The 
water-wheel, wind-mill, and electric motor are engines for 
utilizing other energy than that of heat, but in each of these 
cases the energy may be traced to heat. The water was 
raised from the sea by the heat of the sun, and wind is caused 
by heat from the same source. The electric motor uses 
current furnished by a dynamo, which in its turn, if not 
driven by wind or water, uses energy from a steam engine 
or some other machine driven by artificial heat. 

520. Steam Engine. Historical Note. Most important of 
the various forms of engines which utilize heat energy for 
doing useful work is the steam engine. It was invented in 
England late in the seventeenth century. The earlier forms 
were used for pumping water from the mines which are such 
an important factor in the industrial greatness of England. 
For a century the development of the steam engine was 
very slow, but about 1775 many important improvements 
were made by James Watt. 1 To such a degree of efficiency 

1 James Watt, 1736-1819. Scotch inventor. 



HIGH-PRESSURE EXGIXE 



253 



was it brought by this mechanical genius that the engines 
which drove the mills and factories of Europe and America 
remained for a century in nearly all important respects 
unchanged. Steam was first used in navigation by Robert 
Fulton, 1 in 1807, and the first successful locomotive was 
made in 1829 by George Stephenson. 2 

521. High-pressure Engine. The diagram shows the essen- 
tial parts of the simple steam engine. The steam-chest N 
and cylinder M are shown in cross-section and the other 
parts are represented simply by lines. In Fig, 270 steam 





Fig. 270 



Fig. 271 



is being admitted from the boiler by the pipe S, through the 
steam chest and the "port" B to the right-hand end of the 
cylinder. Here it exerts a pressure of many kilograms per 
square centimeter upon the piston P, forcing it toward the 
left. The piston rod G slides through a tightly fitting 
joint into the cylinder, drawing the crank C, by means of 
the connecting rod R, and causing the wheel to turn as shown 
by the arrow. Meanwhile steam from the left-hand end of 
the cylinder is escaping by the port A and the exhaust 
(shown midway between A and B) into the atmosphere. 
When the piston reaches the end of its stroke toward the 
left, the slide valve D, actuated by the eccentric E, the rod 
H , the lever L, pivoted at T, and the rod K, has moved to 
the position shown in Fig. 271, allowing the steam to enter 



1 Robert Fulton, 1765-1815. American inventor. 

2 George Stephenson, 1781-1848. Eminent English engineer, 
railroads, designed bridges, and invented the tubular boiler. 



Built 



254 HEAT 

the left-hand end of the cylinder and to escape from the right- 
hand end. 

522. To regulate the speed, various kinds of governors 
are used. The best of these are so arranged that when 
the load is light, they shut off the steam in the early part of 
the stroke and thus permit the steam which has been admitted 
to push the piston the remaining distance by expanding. 
On locomotives the "cut-off" is regulated by hand, much 
more steam being used in starting the train than in keeping 
it going. Some modern "automatic cut-off" engines do not 
use the slide-valve. 

523. The Low-pressure Engine, or condensing engine, is 
used where a great quantity of power is needed. It is more 
expensive to build, but more economical to operate. In- 
stead of forcing the escape steam out into the atmosphere 
against a pressure of about 1 kilogram per square centimeter, 
it is sent into a cooled chamber where its condensation pro- 
duces almost a vacuum. In flowing into this condenser it 
has almost no pressure to overcome, and thus there is a great 
saving of energy. A further saving is due to the fact that 
this condensed steam is pumped back into the boiler hot, 
thus saving the coal necessary to heat a fresh quantity of 
water to the boiling point. Steamships use condensing 
engines. Those which cross the ocean are obliged to do so, 
in order to save the fresh water which is necessary for all 
steam-boilers. The locomotive takes on a water supply 
every hour or two, but the ocean steamer, if it used a high- 
pressure engine, would have to carry so much water that it 
would seriously decrease its room for cargo. The locomotive, 
on the other hand, cannot afford to carry the extra machinery 
necessary for the condenser. 

524. The Efficiency of the Steam Engine is necessarily very 
small, because the large amount of heat necessary to 
evaporate the water is all thrown out into the air with the 
steam in the case of the high-pressure engine, or flows away 
in the water used to cool the condenser in the case of the low- 
pressure engine. Sometimes where high-pressure engines 



STEAM TURBIXES 



255 



are used in electric-light ''plants/' the exhaust steam 
is turned into street mains for heating buildings in the town. 
If we consider simply the proportion of the energy of the 
coal which is converted into mechanical work, the percentage 
of efficiency seldom reaches 20 per cent. The ocean steamer 
uses one-fifth of the energy of its coal to propel it and the 
other four-fifths to heat the ocean and the atmosphere. 

525. Steam Turbines. The ordinary forms of steam engine 
lose some energy, especially at high speeds, on account of 
the inertia of the parts which move backward and forward. 
In an engine which makes 20 or 30 revolutions per minute, 
loss from this cause is small; but if the speed be 300 revolu- 
tions per minute the kinetic energy of the piston and other 
moving parts is considerable. Since the kinetic energy is 
J mv 2 , the work done in starting and stopping the piston at 
300 revolutions per minute is 100 
times as much as at 30 revolutions. 
It has therefore long been the aim of 
inventors to produce a steam engine 
without "reciprocating parts," as the 
piston and its accompanying parts 
are called. The result of this effort 
is the steam turbine, which utilizes 
the kinetic energy of steam in much 
the same manner that the water tur- 
bine makes use of that of water. The 
plan of a simple steam turbine is 
given in the diagram. A is a metal disk, revolving on a 
shaft. Nozzles N convey steam to a row of holes near 
the circumference of the disk. After passing through the 
holes in the revolving disk, the steam must pass through 
holes in a fixed disk B beyond it. The course of the steam 
through nozzles and holes is shown in the detail diagram 
at the right, where C is a nozzle, D is the revolving disk with 
its curved holes, and E the stationary blades. In large 
turbines many sets of moving and stationary blades are 
used. 






AB 




Fig. 272 



256 HEAT 

526. Gas and Gasoline Engines are used in many places 
where comparatively small power is required, and it is 
desirable that the engine be capable of being quickly started. 
If a steam engine has not been in use, it requires some 
time to "get up steam." The gas engine uses any form of 
combustible gas, which is mixed with air in the proper 
proportions to make an explosive mixture, and exploded in 
the cylinder of the engine by an electric spark or other 
device. Such engines are commonly "single-acting," that 
is, the explosions push the piston in only one direction, a 
heavy fly-wheel being used to carry the piston back by its 
inertia. When gasoline is used instead of gas, it is vaporized 
or atomized by a current of air, and the vapor used in the 
same manner as gas. The cylinder is cooled by water circu- 
lating around it, or in the case of some automobile motors by 
air. This is necessary, because the heat of the explosions 
would soon heat the cylinder beyond the limit of safety. 
Gasoline motors are satisfactory where a portable engine is 
used for threshing, etc., because they require less attention 
than a steam engine while in operation, and less transporta- 
tion of water and fuel. 



EXERCISES AND PROBLEMS. 

1. On a cold day why does an iron fence-post feel colder 
than a wooden one? 

2. A "brick" of ice-cream in a paper box, wrapped in 
many thicknesses of newspaper will keep unmelted for several 
hours in a warm room. Why ? 

3. Why are tight-fitting gloves less warm than loose ones? 

4. Should metal vessels in which tea and coffee are placed 
on table be polished or not? 

5. In stirring hot coffee, what difference would you observe 
between a solid silver spoon and a plated one? 

6. Why does carpet feel warmer to bare feet than oilcloth ? 

7. The moon rotates on its axis in about 27 days. It has 
no atmosphere, so far as known. How would the difference 



EXERCISES AND PROBLEMS 257 

in temperature of the moons surface on the bright and dark 
sides compare with the difference in temperature between 
day and night on the earth? 

8. For out-door summer wear, clothing of what color is 
most likely to be comfortable? 

9. Is it a good plan to use cooking utensils with polished 
bottoms ? 

10. On a bright summer day an attic under a slate roof 
is very hot. Is this because the slates transmit solar radia- 
tion? What do they do? 

11. Are cloudy winter nights likely to be as cold as clear 
ones? State reason for your answer. 

12. A locomotive has two cylinders. The pistons each 
have an area of 250 square inches and move backward and 
forward a distance of 2\ feet. The steam pressure in boiler 
and cylinders is 150 lbs. per square inch. In starting, full 
pressure is used for the whole stroke. When the wheels 
make one revolution in four seconds, how many horse-power 
is the locomotive developing? 

13. If one puts one hand into ice-water and the other 
at the same time into water as hot as he can bear, what will 
be observed if both hands are transferred quickly into a 
vessel of lukewarm water? 

14. Where stones project out of the snow, melting is more 
rapid than where the snow is unbroken. Why is this? 

15. Is the air under a tree likely to be cooler than that 
in the sunshine near by? 

16. Why does a thermometer show a higher temperature 
in the sun than in the shade? 



17 



CHAPTEE IX. 

MAGNETISM. 

527. Natural Magnets. One of the ores of iron is called 
magnetite, or magnetic oxide of iron. It is so called because 
some pieces of it are magnets, that is, they attract iron 
objects. Such pieces are also called loadstone (sometimes 
spelled lodestone). The name magnet is said to be derived 
from Magnesia, a country near the Black Sea, from which 
natural magnets were brought to Europe in ancient times. 

528. All objects attract all other objects with the force 
of gravity,- but this attraction on the part of small bodies is 
so small as to be discovered only with the greatest difficulty. 
Magnetic attraction is far stronger, and is manifested by only 
a few things. Iron, nickel, cobalt, and a few of their com- 
pounds and liquid oxygen were until recently the only known 
substances 1 which are strongly attracted by a magnet. The 
nickel of a 5-cent piece will not serve as an example, since 
the coin is only one-quarter nickel. 

529. Magnetization by Induction. A piece of soft iron when 
placed near a magnet becomes itself a magnet by induction, 
but loses the property when the inducing cause is removed. 
A piece of steel (which is iron with a small percentage of 
carbon added) will, under the same circumstances, be less 
strongly magnetized, but will retain its magnetism for an 
indefinite time. A piece of watch spring, a knife blade, or 
other steel object may be quite strongly magnetized by 

1 Hensler's alloys, discovered in 1903, are attracted by the magnet. 
They are composed of copper, manganese, and aluminum. The pro- 
portions, copper 60 per cent., manganese 24 per cent., aluminum 16 
per cent., give an alloy which is nearly as magnetic as nickel. 
(258) 



LARGE MAGNETS 



259 



rubbing it lengthwise over the part of a natural magnet 
where the attractive force is strongest. For a long time 
this was the only known way of making artificial magnets. 

530. Poles. If a magnet be dipped in iron filings, it 
will generally be found that while a considerable quantity 
adhere near the ends of the magnet, few or none cling to the 
middle part. The ends are called the poles of the magnet. 
When suspended so as to move freely a magnet tends to 
point north and south. The north-pointing end is called 
the north pole of the magnet, and the other its south pole. In 
magnetizing a piece of steel it must be drawn always in the 
same direction across the pole of the magnetizing magnet, 
which should be considerably larger than the piece of steel to 
be magnetized. It will be found that the end of the piece of 
steel which last touched the magnet is a pole of the kind oppo- 
site to that over which it was rubbed. If the new magnet be 
now rubbed in the opposite direction over the pole on which it 
was magnetized each stroke will weaken its magnetism, and if 
the process be continued it will be demagnetized and finally 
again magnetized with poles reversed. If, however, after a 
piece of steel has been magnetized by drawing it over one 
pole of a magnet, it be drawn in the 
other direction over the other pole, 
the tendency will be to strengthen its 
magnetism. The magnetizing magnet 
will, in general, lose none of its mag- 
netic strength in the process. 

531. Large Magnets. A thin piece 
of steel can be magnetized more 
strongly in proportion to its weight 
than a thicker piece. It is a good 
plan, therefore, in making a large 
magnet to use a number of thin 
pieces, magnetize them separately 
and fasten them together. Magnets are sometimes made 
of horseshoe shape, so that both poles may be made 
to attract the same object at the same time. Horse- 




Fig. 273. — Compound 
horseshoe magnet with 
armature. 



( 



J 

260 MAGNETISM 

shoe magnets are generally furnished with a piece of soft 
iron to be kept attached to the poles when the magnet is 
not in use. This is called an armature or keeper (A, Fig. 273). 
It tends to prevent the magnet from becoming gradually 
weaker. Different kinds of steel vary very much in the 
amount of magnetic force which they can exert, and in the 
permanence of their strength. Sometimes, as in the tele- 
phone receiver, there is a separate pole piece of soft iron 
bolted to the pieces of steel. Certain kinds of cast iron 
are also capable of retaining magnetism, and magnets made 
of this material are used in some galvanometers. The 
most powerful magnets are made with soft iron cores, 
surrounded with many turns of insulated wire carrying a 
strong electric current. Electro-magnets will be further 
described later. 

532. Law of Magnetic Action. If a magnet be suspended 
and one pole of another magnet be brought slowly near first 
to one pole and then to the other of the suspended one, it 
will be found to repel one and attract the other. If now the 
second magnet be suspended, the pole which repelled the 
north pole of the other will itself point north. Like poles 
repel each other and unlike poles attract each other. The 
force between any two poles varies in accordance with a law 
precisely similar to that of gravitation; it is directly pro- 
portional to the product of their strengths, and inversely to 
the square of the distance between them. If the distance be 
doubled, the force will be \ as great; at 3 times the distance 
the force will be \ as great, and so on. If the two magnets 
used in such an experiment differ very much in strength, a 
curious paradox may be observed. If the two north poles 
are brought slowly toward each other, they will presently 
repel each other. But if they be brought quickly quite near, 
they will attract each other. This is because the stronger 
magnet induces in the end of the weaker which is nearest 
to itself a pole of opposite kind to the inducing pole, and so 
attracts the weaker magnet, while at a greater distance it 
repelled it. 



NATURE OF MAGNETISM 261 

533. Unit Pole. In order to measure the strength of 
magnets it is necessary to adopt some unit. A unit pole is 
denned as one that will repel one of the same name and 
strength at unit distance (one cm.) with unit force (one 
dyne). Of course we can never have a single pole. Every 
north pole must have a corresponding south pole. It is 
possible by special devices to magnetize a bar so as to have 
like poles at the ends and one of the opposite sort in the 
middle, but one pole alone is impossible. The best approxi- 
mation we can make is by magnetizing a long and very 
slender cylindrical steel bar. Such a magnet has its attract- 
ing force concentrated very close to the ends, so that the 
distance of two such poles from each other can be measured 
with tolerable accuracy. In large bars the poles are some- 
what diffused, the force being shown at a considerable distance 
from the ends. 

534. Nature of Magnetism. If a magnet be broken, each 
of the parts will have two poles, nearly as strong as those of 
the original magnet. This may be well shown with a mag- 
netized piece of watch spring. However large the number 
of pieces into which such a magnet is broken, each is a per- 
fect magnet. This fact seems to indicate that magnetism 
resides in every smallest particle of the steel. The reason 
why no attraction for outside objects is exerted at the middle 
of the bar may be shown by placing two equal and opposite 
poles in close contact and dipping them in iron filings. 
The two will pick up a much smaller bunch than either one 
separately. Each pole is exerting the greater part of its 
force upon the other pole, and so has little left with which 
to attract outside things. So, in the middle of a magnetized 
bar we may imagine each molecule to have its north pole 
against a south pole of equal strength, and that they exactly 
neutralize each other, so to speak. 

535. If a magnet be heated red hot, its magnetism is 
destroyed. This seems to show that magnetism is a matter 
of arrangement of the molecules. Heat is molecular motion, 
and the effect of setting the molecules into violent motion 



262 MAGNETISM 

would naturally be to destroy any arrangement which they 
had before being heated. 

536. If a test-tube nearly filled with steel filings be 
subjected to a magnetizing force, preferably by inserting 
it in a coil carrying a strong electric current, it will be found 
that the whole mass behaves like a magnet. 1 This is best 
shown by bringing one end of the tube slowly toward one 
end of a suspended magnet. If repulsion is observed, the 
poles are similar, but attraction would not prove the filings 
magnetic, since a non-magnetic bar would produce the same 
effect. If attraction is observed on a first trial, therefore, 
the same end of the tube must be presented to the other 
end of the magnet, which it will be found to repel. If the 
tube be now shaken thoroughly, so as to disarrange the filings, 
the closed end of the test-tube will be found to attract either 
end of the suspended magnet, showing that the polarity 
has been destroyed. This result seems quite similar to that 
obtained by heating a magnetized bar red hot. 

537. If the electric current passing through the coils of 
an electro-magnet be interrupted, the iron core may be 
heard to give a distinct click, each time the circuit is opened 
or closed. This fact seems to indicate that the molecules of 
the iron change their arrangement when the core is mag- 
netized or demagnetized. 

538. These experiments and many others seem to justify 
the conclusions that magnetism resides in the molecules 
of the iron or steel, and that it depends upon some arrangement 
of those molecules. We may imagine that each molecule is 
a tiny magnet, that when the bar is neutral the molecules 
point in all possible directions and that when it is fully mag- 
netized they all point in the same direction. 

1 If we wish to test the magnetic condition of a piece of iron or steel, 
the method described above is much more satisfactory than to dip 
it in iron filings. It may be too feebly magnetic to pick up a single 
filing, and yet show its polarity by repelling the like pole of a suspended 
magnet. On the other hand, the filings themselves may be magnetic, 
and so able to cling to a non-magnetic piece of iron. 



THE EARTH A MAGNET 263 

539. Lines of Magnetic Force. If a magnet be laid on a 
table between two boards as thick as itself, a smooth sheet 
of paper laid over it, iron filings sprinkled on the paper, and 
the paper slightly tapped, the iron filings will arrange 
themselves in fairly definite lines (see Fig. 276) called by 
Faraday, "Lines of Magnetic Force." If a small compass 
needle be placed at any point on the paper, it will point 
in the same direction as the lines of arrangement of the filings 
at that point. A line of force may thus be defined as a line 
showing the direction of the resultant of all the magnetic forces 
acting at that point. If we imagine a free north pole, that is, 
a north pole not connected with any south pole, placed 
near a magnet and free to move, it would move along a line 
of force to the south pole of the magnet. Any space con- 
taining lines of magnetic force is called a magnetic field. 

540. The Earth a Magnet. Allusion has already been made 
to the fact that a suspended magnet entirely away from other 
magnets points north and south. This indicates that the 
earth has lines of force and is therefore a magnet. Another 
evidence of the magnetic character of the earth is given by 
the following very striking experiment : Take a bar of steel 1 
a foot or more in length, and test its magnetic condition as 
described in paragraph 536. If it is found to be magnetic, 
mark the north pole (a chalk mark does very well). Now 
hold the bar with its south pole pointing north, and sloping 
downward at an angle of 60° or more. Strike the upturned 
end a sharp blow with a hammer. The end which was a 
north pole will probably now be found to be a south pole. 
If it is not so, repeat, striking it several times. The polarity 
may be reversed as often as desired by reversing the direction 
of the bar and striking it again. This result seems to show 
that the earth is a magnet, since it is able to render a piece 

1 Any bar of steel not sufficiently magnetic to pick up iron filings 
will do. It need not be good steel. A piece of gas pipe or any so-called 
iron rod answers very well. A strip of sheet "tin" held in the proper 
position and then bent slightly shows the same results. 



264 



MAGNETISM 



of steel magnetic. It also indicates that the magnetic 
property depends upon the arrangement of the molecules. 
They are jarred by the hammer blow, and the magnetic 
force of the earth tends to arrange them with their north 
poles north. A further confirmation is given by holding 
the bar east and west and striking a number of blows. By 
care and repeated tests the bar may by this means be almost 
perfectly demagnetized; or, to speak more accurately, it 
may be brought to such a state that neither end behaves like 
either a north or a south pole. Very careful tests might 
show that one side of the bar is a south and the other a 
north pole. This experiment illustrates forcibly why it 
injures magnets to drop them or to use them for hammers. 

541. The Compass. The tendency of the magnet to point 
north and south has been known to Europeans since some 
time in the fifteenth century. The mariner's compass 
made possible the voyages of discovery of that period, 




Fig. 274. — Mariner's compass. 

and is still of the greatest importance to navigators. It 
consists essentially of a magnet fastened to a circular card 
and balanced upon a point. On the card are marked the 
" points of the compass," including besides the " cardinal 



DECLINATION 265 

points," North, South, East, and West, many intermediate 
ones. Between North and West the points are as follows: 
North; North by West; North Northwest; Northwest by 
North; Northwest; Northwest by West; West Northwest; 
West by North; West. The other quarters are similarly 
divided. In Fig. 274, the card is divided into half " points." 
Each whole point as from North to North by West, includes 
11 J degrees. A fixed index point on the box, at the circum- 
ference of the card, by means of the mark on the card 
which comes opposite to it, shows in what direction the ship 
is sailing. In Fig. 274 the direction indicated is nearly 
northeast. The compass is mounted in pivoted rings called 
gimbals, in such a manner that it will remain horizontal in 
whatever direction the ship rolls. In measuring the areas of 
farms and for other allied uses an instrument is employed 
called the surveyor's compass. It has a pivoted magnet 
with sharpened ends, and a circle divided into degrees, 
numbered from the North and South, points both ways 
to 90°. 

542. Declination. The direction of the magnetic needle at 
most places on the earth's surface is not exactly north and 
south. The difference between true north and magnetic 
north, measured in degrees, is called the magnetic declina- 
tion, or sometimes " variation of the compass." The direc- 
tion of the compass at a given place is not always the 
same. It is subject to daily and yearly changes so slight as 
to have no practical importance. The "secular variation," 
however, is very great. In London, the declination in 1580 
was 11° East. In 1816 it was 24|° West, and is now about 
16° West. It seems to be going through a long cycle of 
changes which has not been completed since the first observa- 
tions were made. The declination at Philadelphia in 1908 is 
nearly 8° West. The line of no declination in 1900 crossed 
the states of Michigan, Ohio, Kentucky, Tennessee, North 
Carolina and South Carolina. West of this line the declina- 
tion is toward the East. Columbus on his first voyage crossed 
the line of no declination somewhere on the Atlantic. 



266 



MAGNETISM 




Fig. 275. — Dipping needle. 



543. Dip. If a bar of steel be carefully pivoted at its 
centre of gravity so as to be able to swing in both a horizontal 
and a vertical plane, and then magnetized, it will not only 
point north and south, but will, in general, not remain 
horizontal (Fig. 275). At Philadelphia the deviation from 
the horizontal is now about 
70°. This angle is called 
the " magnetic dip." At 
two points on the earth's 
surface the dip is 90 ° ; that 
is, the needle stands ver- 
tical. These are the North 
and South magnetic poles. 
The North magnetic pole 
is in about latitude 70° 
North and longitude 97° 
West from Greenwich. It 
was discovered in 1831 by 
Sir John Ross. A set of 
observations were taken recently in the same region by 
Roald Amundsen, a Norwegian explorer, but no results 
have yet been published, so it is not yet known whether 
the pole has shifted between 1831 and 1905. The South 
magnetic pole has never been reached, although Dr. Frederick 
A. Cook reached a point on the antarctic continent due 
south of the pole in 1903. It is in Victoria Land, about 
latitude 75° South and longitude 153° East. 

544. At the North magnetic pole the north pole of a " dip- 
ping needle" points straight down, as the south pole of the 
needle would do at the South magnetic pole. The poles of 
the earth are opposite in kind to the poles of the magnet 
which point toward them, but this need not lead to confusion 
of terms. The North magnetic pole of the earth is opposite 
in kind to the north pole (sometimes called north pointing 
pole) of a magnet, but we seldom have occasion to speak of 
the earth's magnetic poles, and when we do we may name 
them at full length, and so not leave room for confusion. 



COMPLEX MAGNETIC FIELDS 267 

545. The measurement of declination may be made with 
tolerable accuracy by means of an ordinary surveyor's 
compass, but the measurement of dip is a complex and 
difficult process. 

546. Magnetic Storms. Sometimes small disturbances of 
the magnetic needle are observed at the same time over large 
areas. These disturbances are called magnetic storms. 
They are apt to occur at times when many sun-spots are 
visible, and it is supposed that the forces which produce the 
sun-spots send out ether waves which travel across the inter- 
vening space and produce the magnetic storms. 

547. Strength of Magnetic Fields. At any point of a mag- 
netic field the "strength" is the force in dynes which the 
field would exert upon a unit pole placed at the point, urging 
it along the lines of force. For instance, if at a point near 
the north pole of a magnet, a unit south pole is attracted 
with a force of 15 dynes, the strength of the field at that 
point is 15 units. It is convenient to represent a unit field by 
imagining one fine of force per square centimeter to pass 
through a surface perpendicular to the lines of force at the 
point. Then a field of 15 units would have 15 lines per 
square centimeter. At a point nearer to the magnet the 
number of lines per square centimeter would be greater 
because of the convergence of the lines toward the pole. 
Of course the lines converge toward a stronger part of the 
field, and a part toward which they diverge is weaker. A 
uniform field would have parallel lines of force, distributed at 
equal distances. 

548. Complex Magnetic Fields. The simplest field which 
we can examine is that of the earth, which for such distances 
as we consider in laboratory experiments is practically 
uniform. If we examine the field near a strong magnet we 
do not distinguish the earth's influence at all, but as we 
recede from the magnet, the modifying effect of the earth's 
field becomes more and more manifest. A convenient 
method of exploring such a field is by means of a small 
compass. If a bar magnet be laid on a sheet of paper and 



268 MAGNETISM 

the small compass placed near its north pole, the needle shows 
the direction of a line of force there. If now we make a 
dot at each end of the needle, and then move the compass so 
that the south pole is where the north pole was before, 
then make a dot at the new position of the north pole, and 
so on, we shall trace a line of force, which will either curve 
around to the south pole of the magnet or run off into the 
earth's field. By continuing this process we may trace 
as many lines as we choose. The figures show several 




Lines of force about a bar magnet. 
Fig. 276. — North pole pointing Fig. 277. — North pole pointing 

South. North. 

maps of such fields. The shape of the lines of force is repre- 
sented with fair accuracy, but their relative number at dif- 
ferent parts of the field is not. The fact that those which are 
drawn converge toward a stronger part of the field is well 
shown. The points marked X are neutral points, at which 
the resultant of all the magnetic forces is zero. Nearer 
to the magnet the direction of the needle is controlled by the 
magnet. Farther away it is controlled by the earth. At 
the neutral point the forces of the earth and magnet are 
equal and opposite. 

549. Magnetic Permeability. If a piece of soft iron be 
placed near the pole of a magnet, the strength of the field 
beyond the piece of iron will be much diminished. The 



N 




I 




B 


N 




n 

Fig. 


278 



PROBLEMS AND EXERCISES 269 

piece of iron forms a sort of magnetic shield/ seeming to 
cut off the influence of the magnet in somewhat the same 
way that an opaque body shuts off light. We may imagine 
that the iron absorbs lines of force as opaque bodies absorb 

light. This property of the ^ 

iron is expressed briefly by say- 
ing that it has high magnetic 
permeability. In I, an object 
placed at A would be attracted 
more strongly than in II, the 
iron bar B having been placed 
between A and the pole. Iron 
seems to attract lines of force, 
and we imagine all the lines of 
a field to be closed curves. In 
the case of a bar magnet, a line leaving a north pole may 
curve around to the south pole and return to the point of 
starting through the steel bar. If, however, it starts from 
the north pole of one magnet and reaches the south pole 
of another, or runs off into the earth's field, its course may 
be very complex and difficult to trace. 

PROBLEMS AND EXERCISES. 

1. Two equal N. poles at a distance of 1 meter exert on 
each other a force of .01 gram. What is the strength of each? 

2. Why does the use of the mariner's compass on board 
steel ships involve special precautions? 

3. How would you prove two magnets to be of equal 
strength ? 

4. A pole with strength 50 units exerts a force of 7 dynes on 
another pole 10 cm. away. What is the strength of the second ? 

5. With what force will a pole of 50 units strength act on 
a pole of 10 units at a distance of 50 cm. ? 

1 Watches which are brought near to strong magnets may be injured 
by the magnetization of their hair-springs and other steel parts. Elec- 
tricians often use watches protected by soft iron cases. 



CHAPTER X. 

STATIC ELECTRICITY. 

550. Electrification. If we rub a cat in cold weather, 
sparks are often produced. The same effect is sometimes 
observed when dry hair is combed with a hard rubber 
comb, or when we take off a woollen garment. We may also 
notice the attraction of the comb for the hair, and of the hand 
for the fur of the cat. When a carpenter's plane is used 
in cold weather, the shavings often stick to the plane, the 
bench and the hands. We describe the condition of objects 
which thus attract each other by saying that the attracting 
bodies have been electrified by friction, or that one of them 
has been electrified. 

551. If a pencil eraser be rubbed on a woollen garment, 
it will, unless the atmosphere be very damp, pick up a tiny 
scrap of dry paper. A rectangular strip of newspaper of 
convenient size (say 6 cm. X 20 cm.), drawn between two 
woollen surfaces, will adhere to the wall or a window pane or 
even to the face. Unglazed paper somewhat heavier than 
newspaper is better for this experiment, which succeeds 
only when the air is in a favorable condition. Such a 
condition is generally found in a warm room in dry winter 
weather. It seems, however, to be not the temperature 
or dryness which is essential, but some other condition 
dependent upon these. (See paragraph 708.) 

To Thales (Greek philosopher, 600 B. C.) is ascribed the 
discovery that a piece of amber which had been rubbed 
would pick up light objects. The Greek name for amber 
is elektron, and from this the word electricity is derived. 
(270) 



CONDUCTORS AND INSULATORS 271 

552. Attraction and Repulsion. In the figure, A is a glass 
tube or rod suspended by a wire hook and silk thread from 
any convenient support. If another 
glass tube which has been rubbed with 
silk be brought near one end of the 
suspended one, it will be attracted. 

The same effect is produced if a wooden 

rod or any other object be suspended F 27Q 

in the hook. It is thus shown that 

electrical attraction is exerted upon all objects without 
reference to their mass or material. 

553. If now a glass tube be rubbed with silk and sus- 
pended, and the other glass tube, also rubbed with silk, 
be brought near the suspended one, they will be found to 
repel each other. Exactly similar results are obtained if we 
substitute for the glass tubes rods of hard rubber or sealing 
wax, rubbed with catskin or flannel. If, however, a rubber 
rod which has been rubbed with cat-fur be brought near to 
a suspended glass tube which has been rubbed with silk, 
they will be found to attract each other quite strongly. 

554. Positive and Negative. This difference between the 
glass and rubber we denote by saying that the glass is posi- 
tively electrified and the rubber negatively. We are using 
the words positive and negative as they are used in algebra, 
to denote oppositeness in one respect on the part of things 
which are alike in several respects. Of course there is no 
reason why glass should not be said to be negatively electri- 
fied by being rubbed with silk, but as in the case of many 
other conventional terms, it is important to remember how 
they are actually used. 

555. Conductors and Insulators. If a rod of metal with 
rounded ends be rubbed, instead of glass or rubber, no 
evidence of electrification will be found. If, however, 
the metal rod be held by a glass handle, it may be electrified 
by rubbing, although not so strongly as glass or rubber. 
When the metal rod is held in the hand, the electrification 
escapes into the body, but when the piece of glass is between 



272 



STATIC ELECTRICITY 



the hand and the rod, the electrification cannot escape. 
We describe this difference by calling glass a non-conductor 
or insulator, and the metal a conductor. All metals are 
good conductors compared with other things. Among the 
best insulators are ordinary glass, silk, rubber, porcelain, 
mica, shellac, and other gums. Under some conditions 
gases are insulators also. 

556. Charged Bodies. If a conductor be supported by a 
non-conductor, it may be electrified either by rubbing it or 
by touching it with a body which has been rubbed. Such 
a body is said to be charged. If an electrified rubber rod 
be brought near to a pith ball suspended by a silk thread, 
it will be attracted by the rod, touch it, be charged nega- 





Fig. 280 



Fig. 281 



tively from the rod, and will then be repelled by the rubber 
(Fig. 280). If now a glass tube electrified by rubbing it 
with silk be brought near the pith ball, it will be attracted 
(Fig. 281). This experiment illustrates again that bodies 
similarly electrified repel each other; those oppositely electri- 
fied attract each other. 

In the pith ball experiment it is well to have two pith 
balls suspended by silk threads. When the two balls are 
similarly electrified they will hang apart. 



TO DISTINGUISH POSITIVE FROM NEGATIVE 273 

557. Two-fluid Theory. The terms commonly used in 
describing electrical phenomena are those of the two-fluid 
theory, which assumes that electricity is a material thing, and 
that there are two kinds: positive and negative. In using 
the terms employed by this theory, we do not commit our- 
selves to a belief in the theory, any more than we admit 
Newton's theory of light when we speak of light rays. The 
two-fluid theory assumes that a neutral body contains equal 
quantities of positive and negative electricity, and that an 
electrified or charged body has an excess of one kind or 
the other. The total quantity of electricity contained in 
a body is supposed to be unchangeable, so that when some 
negative is taken away from a body, the same act gives to 
the body a quantity of positive equal in amount to the nega- 
tive which was taken away. It is not likely that this theory 
is true, but it is consistent with the facts, and we may con- 
veniently describe electrical phenomena by the use of its 
terms. Some discussion of the most recent theories of elec- 
tricity will be given at the end of the book in connection 
with radio-activity. 

558. To Distinguish Positive from Negative. The suspended 
pith ball offers a convenient mode of determining which 
kind of electricity is present in a charged body. Suppose 
a piece of glass has been rubbed with catskin and we wish 
to test it. If it repels a pith ball which has been charged 
by touching it with a rubber rod electrified with catskin, 
we may know that the glass is negatively electrified. If 
the pith ball is attracted, the result is inconclusive, for the 
charged ball would be drawn by its own attraction toward 
a neutral body. If, then, the negative pith ball is attracted, 
we must make a further test by charging the pith ball posi- 
tively from glass rubbed with silk and again presenting the 
glass rubbed with catskin. If the ball is now repelled we are 
sure that the glass was positively electrified by being rubbed 
with catskin. Rubbing with catskin produces positive 
electrification upon some glass tubes and negative upon 
others. 

18 



274 



STATIC ELECTRICITY 




Fig. 282.- Gold-leaf 
electroscope. 



559. Both Kinds Produced at the Same Time. A catskin 
tied to a rubber or glass rod and then rubbed against a 
rubber rod, will be found to be positive. In general, when 
two substances are rubbed together, one of them is electri- 
fied positively and the other negatively. In most instances 
the electricity escapes without being detected. 

560. The Gold-leaf Electroscope is a much more delicate 
indicator than the insulated pith ball. It consists essen- 
tially of a glass jar through whose cork 
passes a metal rod A, carrying at its 
lower end two small strips of gold leaf 
or other very thin metal leaves, and at 
its upper end a smooth disk of metal, 
D. If the disk be touched by a glass 
rod which has been very slightly electri- 
fied, the gold leaves will diverge and 
remain divergent because they are both 
positively charged and therefore repel 
each other. If a highly electrified body 

is brought near the electroscope, the leaves may repel 
each other so strongly as to be torn. 

561. Electrification by Induction. If an electrified body, 
instead of touching the electroscope, be brought near it 
and then removed, the leaves will at first diverge and then 
drop together again. In Fig. 283 the 
rod is positive, and attracts the negative 
electricity of the electroscope to the top, 
and repels the positive to the bottom. 
The object made up of disk, rod, and gold 
leaves is now said to be electrified by 
induction. It is not neutral, because it 
has an excess of + at one end and of — 
at the other. When the electrified rod is 
taken away, the + and — rush together 
and the electroscope is again neutral. 

If, however, the electrified rod touches the disk, some — 
escapes to the rod, and some + is received from it, and the 
electroscope is left positively charged. 




Fig. 283.— Electrifica- 
tion bv induction. 



COULOMB'S LAW 



275 




562. Neutral, Charged, Electrified by Induction. These 
terms are used in describing the condition of insulated con- 
ductors. A body is neutral when it has 
equal quantities of + and — uniformly 
distributed over it ; electrified by induc- 
tion when there are equal quantities, but 
separated ; charged when it has an excess 
of + or — . The attraction between an 
electrified body and a neutral one seems 
to be due to induced electrification on 
the latter. In the figure the negatively 

electrified rod causes the pith ball to be electrified by induc- 
tion. The side toward the rod being + is attracted more 
than the more remote — side is repelled. 

563. Charge on the Surface. When an 
insulated sphere is charged, all parts of 
the charge repel all other parts, and this 
mutual repulsion keeps the charge on the 
surface and evenly distributed. When the 
charged conductor has a surface of unequal 
curvature, the intensity of the charge is 
greatest where the curvature is greatest. In 
the figure, the charge is most intense at the small end of the egg. 

564. The Charge at a Point becomes so intense that it 
electrifies the adjacent air 1 particles and then repels them, 
thus discharging the body and causing an air current to 
flow away from the point. This flow may be shown by 
holding a lighted candle near the point from which the charge 
is escaping. 

565. Unit Charge. Charges are measured in the same 
manner as magnet poles. If two small bodies having equal 
like charges repel each other at a distance of 1 cm. with a 
force of 1 dyne, each has a unit charge. 

566. Coulomb's Law. Coulomb showed that the attraction 
or repulsion between two charged spheres is directly propor- 

1 It would perhaps be more correct to say that it ionizes the air 
(paragraph 707). 




Fig. 285 



276 STATIC ELECTRICITY 

tional to the product of their charges and inversely to the square 
of the distance between their centres. Two spheres having 
positive charges of 3 and 12 units respectively, whose 
centres are 6 cm. apart, will repel each other with a force 
of one dyne, since (3 X 12) -s- 6 2 = 1. 

567. Potential. When two bodies at different tempera- 
tures are brought in contact, heat flows from the body 
at higher temperature to that at lower temperature. When 
two bodies are connected by a conductor and + electricity 
flows from one to the other, that from which the flow takes 
place is said to be at higher potential than the other. Just 
as difference of temperature is the condition for heat flow 
and difference of level for water flow, so difference of potential 
is the necessary condition for the flow of electricity from 
one point to another, when the two points are joined by a 
conductor. Sometimes when there is very great difference 
of potential between two neighboring points not connected 
by a conductor, electricity passes from one to the other 
across the air, making a disruptive discharge, or, as we are 
accustomed to call it, a spark. 

568. Potential is a Property of a Point, just as level or 
altitude is. The measure of the potential of a point is the 
number of units of work which must be done to bring a 
unit charge of positive electricity to the point from infinite 
distance. It is evident from this definition that a point 
on a negatively charged body is at negative potential, since 
not only would no work be required to bring a positive 
charge to the point, but the positive charge would be able 
to do work in approaching the point. The measure of the 
negative potential would then be the number of units of 
work necessary to remove a unit + charge from the point to 
infinite distance. Since the force required diminishes as the 
square of the distance increases, it becomes so small at great 
distances that in practice a few meters may be regarded as 
infinite distance in considering the potential of small bodies. 

569. Potential of the Earth. In water problems, sea level 
is zero, and points above sea level have positive altitude. 



THE ELECTROPHORUS 



277 



Fig. 286 



Fig. 287 



Water will flow from them into the sea. Such places as the 
Dead Sea and the Salton sink, in California, have negative 
altitude. Water would flow into them from the sea if a 
passage were open. So in electrical problems the earth is 
assumed to have zero potential. Positive electricity in 
any quantity will flow into it, and it will furnish positive 
in any quantity to objects at negative potential. 

570. The Electrophorus. Charging large bodies by means 
of a rubbed glass rod is a very slow process. Of the 
many devices for accumulating charges more rapidly, the 
simplest is the electrophorus. It consists of a plate of 
shellac usually contained in a 
shallow metal pan, and a "lid," 
consisting of a disk of metal or 
of wood covered with tinfoil, 
with a glass or hard-rubber 
handle. When the shellac has 
been negatively electrified by 

rubbing it with catskin, the lid is placed upon it, and we 
have the condition of affairs shown in Fig. 286, where the 
lid is electrified by induction, the lower surface being -f 
and the upper — . The + on the lid and the — on the 
shellac cannot get together because 
except in a few points they are not 
in actual contact, but there is a thin 
layer of air between. The negative 
cannot flow off to the lid at the points 
of contact because the shellac is a 
non-conductor. Thus every little part 
of the negative surface holds some 
positive by attraction across the air 
space. The negative of the lid is 
repelled to the upper surface. If the lid be removed 
by the glass handle without having been otherwise 
touched, it will be found neutral as before. If, however, 
while it is on the shellac, the upper surface be touched 




Fig. 288 



278 STATIC ELECTRICITY 

with the finger, a slight spark is seen, the negative is taken 
off, positive from the body being substituted, and the lid 
is left positively charged (Fig. 287). If it be now lifted 
from the shellac by the insulating handle, and a knuckle 
presented to it, the small + charge is discharged into the 
body (Fig. 288). Since this process leaves the shellac 
negatively electrified, it may be repeated indefinitely, 
any number of sparks being obtained from a single elec- 
trification of the shellac. The energy is supplied by the 
work done in lifting the + lid from the — plate. The 
electrophorus thus illustrates (as do all electrical machines) 
the transformation of energy. 

571. Influence Machines. There are now many kinds 
of machines which work on the principle of the electro- 
phorus, small pieces of metal attached to rotating disks 
of hard rubber or glass being electrified by induction. 
All such are called induction machines or influence machines. 1 
They are used in the treatment of nervous diseases, in 
operating Rontgen-ray apparatus, and for many other 
purposes. 

572. Frictional Machines, in which a glass plate or cylinder 
is rotated between rubbers, were formerly used for experi- 
ments in static electricity. They are far less efficient 
than those of the other type, most of the energy being 
converted into heat. They are more satisfactory than 
induction machines in one respect; the positive always 
collects in the same place. In many influence machines, on 
the contrary, that part of the machine which furnishes 
positive one day may give negative the next. All forms of 
machines provide a place for each kind to accumulate. 
These metal objects are called the terminals of the 
machines. 

1 No description of influence machines is inserted, because there are 
so many types and an explanation of one would not answer for the 
others. Descriptions and explanations will be furnished by the makers 
on request. 



SPECIFIC INDUCTIVE CAPACITY 279 

573. Proof-plane. In order to test the terminals of a 
machine, the little instrument shown in Fig. 289 is used. 
It consists of a smooth metal disk an 

inch or more in diameter, with rounded 
edges, attached to a glass handle. If it 
is charged by contact with one terminal 
of the machine and then brought near 
to a pith ball that has been charged 
from glass or hard rubber, we may easily 
determine which is the + and which C L J ) 
the — terminal of the machine. The p IG 289. Proof- 
proof-plane offers a convenient means of plane, 
testing the charge on any large body. 

574. Condensers. If a piece of tinfoil be pasted on each 
side of a plate of glass, we have a simple form of condenser. 
If one of the tinfoils be charged positively and the other 
negatively, each will hold a much 

larger charge than if it alone were _ 

charged. The negative and positive Fig. 290.— Condenser, 
exert attraction upon each other 

through the glass and hold each other bound. If the 
plate be touched on one side only, a very small part of 
the charge is withdrawn. If both sides be touched at 
once, the experimenter feels a shock, and the condenser 
is discharged through his body. 

575. Specific Inductive Capacity. In general, a condenser 
consists of two conductors separated by an insulator. 1 
The force exerted by the charges upon each other is be- 
lieved to be communicated by a strain in the ether among 
the molecules of the insulator. The amount of force 
communicated differs for different insulators. Similar 
behavior of the ether is concerned in all electrical induc- 

' A charged ball hung by a silk thread in the middle of a room induces 
a charge of opposite kind on the walls of the room, very feeble because so 
widely diffused. The whole room thus makes with the ball a sort 
of condenser, and when one stands on the floor and touches the ball 
the condenser is discharged. 



280 



STATIC ELECTRICITY 



tion, and the differences among insulators in regard to the 
inductive force which they transmit are called differences 
in specific inductive capacity. 

576. The Leyden Jar is a convenient form of condenser. 
It receives its name from the fact that the first one was 
made at the University of Leyden. 1 The usual form is 
as shown in the diagram. Through the cork of a jar passes 
a metal rod having a knob above and a chain below. 
The jar is coated inside and out to within two or three 
inches of the top with tinfoil, and 
the chain touches the inner coating. 
The jar may be charged by connect- 
ing the outer coating by a conductor 
to one terminal of the machine and 
the knob to the other. The inner 
coating will thus receive a charge of 
one kind of electricity and the outer 
one of the opposite kind. As in the 
case of the plate condenser, neither 
charge can be withdrawn separately, 
but if the outer coating be connected 
with the knob by a conductor, the + and — rush together 
and are equally distributed over both coatings, and the jar 
is discharged. It is best to discharge a Leyden through a 
discharger, which may be made of a piece of heavy wire 
with a knob at each end. The discharge may be sent 
through a piece of cardboard, making a hole. 

577. The Electric Spark, to which many allusions have 
been made, generally accompanies the passage of an 
electric charge across an air space. In the case of the 
Leyden jar discharge the spark is quite bright and makes 
a considerable noise. The work done by the discharge 
in forcing its way through the non-conducting air renders 




Fig. 291.— Leyden jar. 



1 A vessel of water was held in the hand and charged by means of a 
chain from a machine. The experimenter removed the chain with his 
other hand and received a shock. 



RESIDUAL CHARGE 281 

the air white hot so that it shines. The sudden expansion 
of the air causes a shock to the surrounding atmosphere, 
just as a small explosion would do, and so we hear a crack. 
An electric spark from a Leyden jar or electrical machine 
does not burn one's knuckles because the quantity of air 
heated is so small. The spark will, however, set fire to 
illuminating gas, or to sulphuric ether. 

578. Physiological Effects of the Discharge. If a jar of 
a liter capacity or more be fully charged and then dis- 
charged through the body by touching the outer coating 
with one hand and the knob with the other, it gives quite a 
painful shock. The muscles are contracted, and a tingling 
pain may be felt for some time in the muscles and joints. 
If a dozen or more persons join hands and pass the dis- 
charge through the bodies of all, the shock is much less 
severe. 

579. The Energy of the Charge Resides in the Glass of 
the condenser. This may be shown by using a Leyden 
jar whose coatings (of heavy tin) are 
removable. When it has been charged 
and set on a glass plate the inner coat- 
ing may be lifted out and then the 
glass lifted out of the outer coating. If 
now the two tin vessels be brought in 
contact nothing is observed. When the 
parts are put together again and the dis- 
charger applied, a vigorous spark occurs. 
If, however, after the jar has been p IG 292.— Separa- 
charged and taken apart, the glass be ble Leyden jar. 
rubbed with the hands, a crackling noise 

is heard, and a prickly sensation is felt. When the glass 
had been rubbed all over and the parts put together again, 
no charge will be found in the jar. 

580. Residual Charge. The important part played by 
the insulator of the condenser is further illustrated by the 
fact that after a jar has been discharged and has stood a 
few moments, a second very small spark may often be 




282 



STATIC ELECTRICITY 



A 



P A 



^ 
/ 



La 



Fig. 293 



obtained. This residual charge seems to soak out of the 
glass, so to speak, and to require a little time to do it. 

581. The Discharge Oscillatory. If a U-tube be filled 
with water and a finger placed over one end, most of the 
water may be poured out of the other side, and we shall 
then have the condition shown in 
I, Fig. 293. The tube is filled 
with water from A to C, held in 
place by the pressure of the atmos- 
phere on the surface C. If now 
the finger be removed from A, 
the water will fall in that side and 
rise in the other, its momentum 
causing it to continue to move 
until it is higher in B than in A, 
as in II, Fig. 293. (If there were 

no friction it would rise in B as high as it had been in A.) 
Then it will fall in B and rise in A, and so oscillate several 
times before it comes to rest at the same level in both arms. 

In like manner the discharge of a condenser is oscillatory. 
The rush from higher to lower potential continues until 
the coating that was negative is at higher potential than 
the other. The process is then reversed, and so on, until 
after perhaps a few thousandths of 
a second, equilibrium is established. 

582. Slow Discharge. A charged 
Leyden jar is placed upon the base 
of an iron retort stand. From a 
metal arm hang a shoe-button, sus- 
pended with silk, and a bell, hung 
by a chain or wire. (The jar must 
have a slight charge, or it will 
immediately discharge by a spark 
from the knob to the bell.) The 
shoe-button is pushed against the knob, which we will 
assume to be +, receiving a + charge, which is repelled 
by the knob, causing the button to strike the bell and be 




Fig. 294. — Slow discharge. 




THE CAUSE OF ATMOSPHERIC ELECTRICITY 283 

discharged, and receive a — charge from the outer coating. 
It then is attracted by the knob and so swings back and 
forth for a long time, discharging the jar 
by slow degrees. It is as if a load of 
coal were carried in one piece at a time 
instead of being dumped into the cellar at 
once. 
- 583. Silent Discharge. If a sharp point 

be connected by a wire with the outer coat- Fig. 295. Silent 

ing of a charged jar, and then brought very discharge, 

slowly near to the knob, the jar may be 
discharged with scarcely any noise. Only a very faint 
buzzing is heard, as the discharge passes from the point. 

584. Franklin's Experiment. There is much about the 
discharge of a large Ley den jar to suggest thunder and 
lightning, and previous to 1752 there had been several 
suggestions that lightning would prove to be an electrical 
phenomenon. In that year Benjamin Franklin, when 
a thunderstorm was beginning, sent up a kite with a linen 
string. He attached a key to the end of the string, and 
held the kite by a silk cord tied to the key. When the 
linen string had been dampened by the falling rain, it 
became a fairly good conductor, and sparks were drawn 
from the key. A Leyden jar was charged and many 
familiar effects were produced. This experiment (which 
is a very dangerous one) was regarded as a proof that 
lightning is an electrical discharge and that thunder 
is simply the crack of a huge electric spark. 

585. The Cause of Atmospheric Electricity is not well 
understood. At high altitudes the air is always at a higher 
potential than near the earth's surface. A cloud collects 
electricity from the non-conducting air much as the coat- 
ing of a Leyden jar collects the charge from the glass, the 
cloud being a conductor, although a poor one. Violent 
electrical storms occur whenever large quantities of moist 
air rise rapidly. The thunderstorms of summer after- 
noons are due to the rapid rise and cooling of large masses 



284 STATIC ELECTRICITY 

of highly heated moist air, the moisture condensing into 
clouds. Tremendous electrical displays occur at the time 
of volcanic eruptions when a column of steam and gases 
rises from the crater. 

586. Effects of Lightning. Discharges from cloud to 
cloud often occur, and these of course cannot do us harm. 
When, however, a discharge passes from a cloud to the 
earth, trees may be shattered, cattle killed, or buildings 
set on fire. A violent lightning stroke sometimes strips 
the bark from a tree. The discharge, meeting with some 
resistance, does work in overcoming it. Heat is produced 
which converts into steam the sap lying between wood 
and bark, and the bark is blown off. The dry materials of 
a barn may be set on fire by heat generated in the same way. 

587. Lightning Rods. When a cloud is highly electrified 
it induces in the earth under it a charge of opposite kind, 
and cloud, air, and earth form a huge condenser. The 
charge often becomes so intense that the air gives way under 
the strain and a lightning stroke occurs. If a number of 
sharp points connected to the earth by good conductors 
are presented toward a charged cloud or body of moist air, 
the discharge will in general take place silently, like that 
of the Leyden jar in Fig. 295, and no damage be done. 
This is the purpose of lightning rods, invented by Benjamin 
Franklin. They should be of ample size, with a number 
of sharp points projecting above the roof at different places. 
At the bottom they must make good connection with moist 
earth. 

588. Discharge through Rarefied Air. If the tube 1 shown 
in Fig. 296 is exhausted so that from ^V ^° -gro" °f an atmos- 
phere remains, and its metal caps are then connected to 



1 The tube commonly used for this purpose contains a cent and a 
feather or some scraps of paper. When it has been exhausted to g^ 
of an atmosphere or less, the light objects fall almost as rapidly as the 
cent, showing that feathers ordinarily fall slowly because of the resist- 
ance of the air. 



EXERCISES AND PROBLEMS 



285 



the terminals of an electrical machine, a silent discharge 
takes place through the rarefied air, which acts as a con- 
ductor (see paragraph 708). If this ex- 
periment be performed in a dark room 
and the discharge passed in successive 
sparks, beautiful color effects may be 
seen. 

589. The Aurora Borealis, or northern 
lights, is supposed to be due to electrical 
discharges through the rare upper atmos- 
phere. In high latitudes auroral displays of 
marvellous beauty are sometimes observed 
during the long winter nights. 

EXERCISES AND PROBLEMS. 

1. Two small spheres are at a distance 
of 10 cm. from centre to centre. One 
has a charge of 10 units of + electricity 
and the other 40 units of — . What is 
the force between them? 

2. A plane is cutting shavings from a 
pine board. The shavings cling to the 

clothing of the workmen. How could you determine whether 
they are + or — ? 

3. A negatively charged body is held near a gold-leaf 
electroscope. While the leaves are divergent a metal ball 
suspended to a silk string is touched to the top of the electro- 
scope. When both ball and charged body are taken away 
the leaves remain divergent. Explain what has happened. 

4. After a thunderstorm several successive telegraph poles 
were found shattered. What had probably happened? 

5. Is it dangerous to carry during a thunderstorm an 
umbrella with a steel stick? 

6. Is it wise to seek shelter under a tree in a thunder- 
storm ? 




Fig. 296.— Aurora 
tube. 



CHAPTEE XI. 

CURRENT ELECTRICITY. 

590. Electric Current, as the term is commonly used, means 
flow of positive electricity. The most characteristic phenom- 
ena of static electricity are attractions and repulsions of 
charges at rest, while the familiar effects of current elec- 
tricity are produced during flow of current. The intrinsic 
differences are matters of degree, not of kind. In their 
behavior electric currents (at least those which flow continu- 
ously in one direction) are almost perfectly analogous to 
currents of water. Electricity flows from a point at higher 
potential to one at lower potential just as water flows from 
a higher to a lower level. Gravity, the force which makes 
water flow, has its counterpart in electromotive force, which 
impels the electricity from higher to lower potential. Elec- 
tromotive force, often abbreviated to E. M. F., is proportional 
to difference of potential. They are measured in the same 
units, and the terms are often used interchangeably. 

591. Galvani and Volta. Galvani, 
a physician of Bologna, was the dis- 
coverer of electric currents (about 
the year 1786). He was experiment- 
ing with the effects of static elec- 
tricity on the muscles of a dead frog, 
and found that if a piece of iron 
touched a muscle of the frog and a 
piece of copper touched a nerve, when 
the iron and copper are joined the 
muscle contracts. Galvani supposed 
this action to be due to electricity 
generated in the body of the frog. 

(286) 




Fig. 297.— Volta's pile. 
Beginning at the top, the 
plates are zinc, paper, 
copper, etc., ten sets. 



POLARIZATION 



287 



Volta, professor in the University of Pavia, contended that it 
was due to the contact of the two metals. The first practicable 
source of current was Volta's Pile, which is a proof of Volta's 
theory. It consists of a number of pairs of plates of copper 
and zinc, separated by paper wet with salt water. Such a 
pile has a difference of potential between its terminals equal 
to the product of the difference of potential of one pair by 
the number of pairs. Current electricity was long called 
by many writers, voltaic electricity. 

592. Simple Cell. One of the means 
employed to furnish electric current in 
the earliest researches was the simple 
cell, which may be made of any two 
metals and an acid or other chemically 
active liquid contained in a suitable 
vessel. A very satisfactory simple cell 
is made by immersing a strip of copper 
and a strip of zinc in very dilute sul- 
phuric acid contained in a glass jar. 
The copper will be at higher potential 
than the zinc, and if they are joined 
by a wire, current will flow through it 
from the copper to the zinc. This 
flow does not discharge the cell, as a 

Ley den jar is discharged, because chemical action in the cell 
furnishes energy to keep up the difference of potential, and 
so the current keeps on flowing. 

The action of the cell in causing flow of current through the 
wires may be likened to the action of a pump raising water 
from one vessel to another, the water flowing back to the 
lower vessel through a pipe as the electricity flows from 
the copper to the zinc through the wire. 

593. Polarization. Sulphuric acid is composed of sulphur, 
oxygen, and hydrogen. The chemical action in the cell 
involves the formation of zinc sulphate by the union of the 
sulphur and oxygen of the sulphuric acid with the zinc, 
and the release of the hydrogen in the form of bubbles which 




Fig. 298.— Simple cell. 



288 CURRENT ELECTRICITY 

accumulate on the copper. If we use ordinary zinc, bubbles 
are released at the surface of the zinc also; but if the zinc 
is pure, bubbles form on the copper alone, and only while 
the wires are joined so as to permit the current to flow. 
This accumulation of bubbles on the copper is called polariza- 
tion. The gas can be collected in an inverted test-tube and 
shown to be hydrogen. Polarization hinders the flow of 
current, and in most forms of cell which are used in practice 
it is wholly or partly prevented by various devices. 

594. Amalgamation of the Zinc by coating the surface with 
a little mercury prevents the acid from acting on it when the 
wires are not joined. The acid acts on impure zinc because 
every bit of iron or carbon embedded in the surface makes 
in effect a tiny separate cell, and little local currents are set 
up at the places where the impurities are. Mercury dissolves 
the zinc and the solution forms a film which coats over the 
impurities. 

595. Circuit. The electricity which flows through the wire 
from the copper to the zinc flows back within the cell from 
the zinc to the copper. The whole path thus traversed by 
the current is called the circuit. To break the circuit means 
to disconnect the conductors at any point so that the current 
cannot flow; to join them again is to make the circuit. The 
part of the circuit outside of the cell is called the external 
circuit. The liquid of the cell is called an electrolyte because 
it is decomposed while the electric current flows through it. 

596. Battery is a term used to denote several cells joined 
together. Sometimes a single cell is called a battery, or 
a battery cell. 

597. Positive and Negative in the Circuit. The wire at- 
tached to the copper plate of a cell is called the positive 
terminal of the cell, and that attached to the zinc the negative 
terminal. If the external circuit be broken at any point, 
that one of the severed ends to which the current will flow 
when they are joined is negative, and that from which current 
will flow is positive. In general, + and — are used to denote 
the direction of flow of current. Current flows from + to — . 



GRAVITY CELL 



289 



In the cell the zinc is + and the copper — because there the 
current flows from zinc to copper. Nearly all cells use zinc 
for the positive plate, and it is well to remember that in 
the external circuit the current follows the alphabetical 
order, flowing toward the zinc from the copper or carbon, or 
silver or platinum, or whatever other plate is used. 

598. Electrolysis means analysis (chemical decomposition) 
by means of electricity. This goes on in any cell which is 
in operation, and many substances are decomposed by the 
passage of electric current through them. One of the first 
things to be separated into parts in 
this manner was water. A simple appa- 
ratus for the electrolysis of water is 
shown in the diagram. A and B are 
platinum terminals. The vessel con- 
tains water to which a few drops of 
sulphuric acid have been added to 
make it a better conductor. Test- 
tubes and H are filled and inverted 
over the platinum terminals. When 
current from a battery of several 
cells is passed through the apparatus, 
bubbles of hydrogen form on the nega- 
tive terminal (or electrode), and bubbles of oxygen on the 
positive. These bubbles collect in the tubes, the hydrogen 
accumulating twice as fast as the oxygen. The negative 
electrode is called the kathode and the positive the anode. 

Substances capable of decomposition by the electric current 
are called electrolytes. To this class belong all acids, and 
solutions of those compounds of metals called bases and salts. 
Hydrogen and metals are called electro-positive because they 
collect on the negative electrode when their compounds 
are electrolyzed. Oxygen and chlorine, on the other hand, 
are electro-negative. 

599. Gravity Cell. Cells for practical purposes, if they are 
to furnish current continuously, must be so made as to avoid 
polarization. In the gravity cell this is done by substituting 

19 




Fig. 299.— Electrolysis 
of water. 



290 



CURRENT ELECTRICITY 




Fig. 300.— Gravity cell. 



for the dilute acid of the simple cell a solution of sulphate of 
copper. The copper sulphate / whose chemical formula is 
CuS0 4 , breaks up into Cu (copper) and S0 4 , the S0 4 uniting 
with the zinc to form ZnS0 4 , as in the simple cell, and the 
copper being deposited on the copper plate. In the simple 
cell the deposit of bubbles of hydrogen 
on the copper hinders the action of 
the cell (chiefly by setting up an E. 
M. F. in the opposite direction), but 
here, since the substance deposited is 
copper, the action goes on unhindered, 
since the conditions remain the same 
as at first. After a time the zinc sul- 
phate which is forming and going into 
solution forms a layer of colorless liquid 
in the upper part of the cell, while the 
lower part contains the blue solution of copper sulphate. 
This separation, which continues while the cell is in action, 
is partly due to gravity, since the blue solution is denser 
than the other; hence, the name of the cell. It is also called 
gravity Daniell, because it is essentially like the Daniell 
cell; crowfoot cell, from the shape of the zinc; and bluestone 
cell, from a name often given to copper sulphate. 

600. In setting up such a cell it is better to put in copper 
sulphate crystals and water than to use a solution of copper 
sulphate. If the solution is used a quantity of copper 
will separate out and be deposited on the zinc. The gravity 
cell works better after having been in use for some time, 
and when not in use it should be connected through a re- 
sistance of at least 10 ohms (paragraph 610) and left working. 
Otherwise the liquids will mix and waste both the zinc and 
the copper sulphate. The gravity cell is used to furnish 
current for telegraphing and for other purposes requiring 
continuous flow of current, or as it is often stated, for closed 
circuit work. 

601. The Daniell Cell has the same liquids as the gravity 
cell, and the same metals: zinc in zinc sulphate solution and 



SINGLE FLUID CELLS 



291 




copper in copper sulphate solution, but they are differently 

arranged, as shown in the diagram, which is a top view. 

The zinc sulphate is contained in 

a porous cup in which stands a 

heavy block of zinc. Immersed 

in copper sulphate solution is 

the copper, in the form of a split 

cylinder surrounding the porous 

cup (C). The porous cup is to 

keep the liquids separated. If 

the cell stands unused they soon FlG ' 301.-Daniell cell (plan). 

mix, and copper is deposited in the pores of the porous cup 

and on the zinc. The action is exactly the same as in the 

gravity cell. The zinc does not need to be amalgamated in 

either. 

602. Other Forms of Two-fluid Cells were formerly used 
where powerful currents were needed, but since dynamos 
(paragraph 660) and storage batteries (paragraph 605) have 
come into use they are not often employed. The Grove 
cell has a strip of platinum immersed in nitric acid contained 
in a porous cup, outside of which is an amalgamated zinc 
cylinder in dilute sulphuric acid. The Bunsen cell is the 
same except for carbon which re- 
places the platinum. In both of 
these the acid surrounding the 
negative plate oxidizes the hydro- 
gen as fast as it is released, and 
thus prevents polarization. 

603. Single Fluid Cells are used 
for many purposes. One of these 
employs carbon and zinc plates 
and a solution of potassium or 
sodium bichromate in dilute sul- 
phuric acid. It does not polarize, 
and on account of its high E. M. F. 
and low internal resistance (para- 
graph 609) is capable of giving a Fig. 302.— Bichromate cell. 




292 



CURRENT ELECTRICITY 



very strong current for a short time. The zinc must be 
amalgamated and so arranged that it can be withdrawn 
from the liquid when the cell is not in use. 

604. The Leclanche Cell, made in various forms and sold 
under trade names, has carbon and amalgamated zinc 
electrodes and a solution of sal ammoniac (ammonium 
chloride). The carbon plate in some forms is surrounded 
by a mixture of powdered charcoal and manganese dioxide 
to prevent polarization. The great advantage of this cell 
consists in the fact that no chemical action goes on when the 
cell is not in use. It is used therefore for open-circuit work, 
such as ringing door-bells where the current flows for only 
a few seconds at a fl 
time. It polarizes * 
if much current is 
drawn from it, but re- 
covers while standing. 

The so-called dry 
cells are of the same 
type. The carbon is 
packed in a mixture 
of powdered carbon 
and manganese diox- 
ide, and the enclosing 
vessel is of zinc, con- 
taining, in some of the forms, a paste, the active constituent 
of which is sal ammoniac, separated by porous paper from the 
mixture about the carbon. The vessel is sealed by pouring 
in melted asphalt, shown at A in Fig. 304. 

605. Storage Batteries. Various forms of " storage" cells 
are in use, all based on the same principle as the original 
one, invented by Plante, in 1860, and improved in 1881. 
In it two lead plates are coated with oxide of lead and im- 
mersed in dilute sulphuric acid. A current is then sent 
through the cell, which electrolyzes the water, liberating 
oxygen at the positive plate and hydrogen at the negative. 
The lead oxide on the negative plate is reduced to lead and 





Fig. 303. — Sal ammo- Fig. 304. — Section 
niac cell. of dry cell. 



ENERGY TRANSFORMATION IN THE CELL 



293 



that on the positive plate is further oxidized to lead peroxide. 
Having been thus "charged," the cell will give a current 
in the opposite direction to 
the charging current, even 
after standing for some 
days or even weeks. In 
A, Fig. 305, the direction of 
charging current is shown 
by the arrow. The + and 
— signs are marked on 
the terminals to show the 
direction of flow from the 
cell. While the cell is fur- 
nishing current, or dis- 
charging, the oxygen is 



| MB 




Fig. 305. — Storage cell. A, beginning 
to be charged; B, charged. 



being transferred from the peroxide across the liquid to the 
spongy lead on the negative plate. The thing stored in the 
cell is chemical energy. 

606. Modern forms of storage cells or "accumulators", 
use other coating substances, and some of them have steel 
plates instead of lead. Their E. M. F. is about twice as great 
as that of a gravity cell. By making the plates large, the 
internal resistance of the cell is made very small, and it will 
furnish very strong current if desired. Care must be taken 
never to discharge a storage battery through a very good 
conductor (i. e., a very low resistance). This is called short- 
circuiting the battery, and it is liable to ruin the battery 
and do other damage in consequence of the heavy current 
flow. 

607. Energy Transformation in the Cell. Since the electric 
current when passed through many substances decomposes 
them in much the same manner in which the liquid of the 
cell is decomposed, and since the chemical action in the cell 
goes on only while the current is flowing, we might be in 
doubt whether the chemical action is the cause or the effect 
of the current. Let us examine the clock, in which the 
wheels move only while the pendulum swings and the weight 



294 CURRENT ELECTRICITY 

descends Which of these is the moving cause? Evidently 
the descending weight. We know it has potential energy 
because we wound it up, and that potential energy is being 
used up as it descends. It is converted into kinetic energy 
of the moving parts and finally into heat. What is being 
used up in the gravity cell? Zinc and copper sulphate. 
They are consumed in much the same way as the coal and 
oxygen under the steam boiler. After the zinc and copper 
sulphate are used up we find that some work has been done 
and some heat developed in the conductors. We are 
justified then in concluding that the materials put into the 
cell possess potential energy, and that this is converted into 
a different form of energy which we call electric current. 
Since the change is accompanied by chemical action in the 
cell, this action may fairly be called the cause of the current. 
Of course in the case of the storage cell the energy is sup- 
plied in the form, not of materials, but of another current. 

608. Resistance. When current flows over a conductor 
it meets with resistance. That is to say, no substance is 
a perfect conductor. Not only does the resistance depend on 
the material of which the conductor is made, but also, of 
course, on its length and cross-section. As we should ex- 
pect, and as is easily shown by experiment, in conductors 
of the same material, resistance is directly proportional to 
length and inversely to area of cross-section. Doubling the 
length doubles the resistance, but using a wire of the same 
length and material but twice the diameter gives a resistance 
only one-fourth as great, since the cross-section is four 
times as great. For wires then we may say resistance 
varies inversely as the square of the diameter. Water pipes 
behave very much like electrical conductors. A large pipe 
permits the water to flow more freely than a small one, and 
a long pipe hinders the flow more than a short one. 

609. Internal Resistance of Cells. The current must 
traverse the liquid in the battery, and suffer resistance 
here as in the other conductors. The internal resistance 
depends on the kind of liquid and on the distance between 



SPECIFIC RESISTANCE OR RESISTIVITY 295 

the plates. In the storage cell the plates are very close to- 
gether, making the resistance very small. The plates are 
also made large, and there is thus a large conductor between 
the plates, which helps to decrease the internal resistance. 

610. The Unit of Resistance is the ohm. It may be defined 
in several ways. For the present it will be sufficient to say 
that it is the resistance offered by a column of pure mercury 
contained in a tube of uniform bore whose cross-section is one 
square millimeter and its length 106.3 centimeters. The 
resistance of copper is much less than that of mercury. A 
copper wire 1 sq. mm. in cross-section and having a resistance 
of 1 ohm is about 64 meters long. No. 18 wire (American 
gauge), which is much used for electric bell connections, is 
about 1 mm. in diameter and has about 50 meters to the ohm. 

611. Specific Resistance, 1 or Resistivity of a substance is 
usually defined as the resistance of a conductor made of the 
substance, 1 cm. long and 1 sq. cm. in cross-section. Pure 
metals in general have less resistance than alloys. Thus 
a mixture of equal parts of silver and copper has a much 
higher resistance than pure silver or pure copper. For 
some purposes wires of high resistance are needed and various 
alloys are made whose resistance is far higher than that of 
any pure solid metal. One of these, manganin, is now gen- 
erally employed in making standards of resistance. 

Table of Resistivity of Metals. 
Resistance of Conductor 1 cm. Long and 1 sq. cm. Cross-section at 0° C, 

in Ohms. 

Silver 0000015 Iron 0000097 

Copper 0000016 Nickel 0000124 

Gold 0000021 Tin 0000132 

Aluminum 0000029 Lead 0000191 

Zinc 0000056 Mercury 0000941 

Platinum 0000090 Manganin 0000410 

1 When this term was first used it meant the resistance of a conductor 
made of the substance compared to that of a similar conductor made 
of silver. Resistivity is a better term, with the present use. 



296 CURRENT ELECTRICITY 

612. Change of Resistance with Temperature. The resist- 
ance of all conductors made of pure metals rises with rise 
of temperature, and if we except mercury, the change per 
Centigrade degree is about 2T3- of the resistance at 0° C. 
This indicates that at — 273° C., the absolute zero, the resis- 
tivity of a pure metal would be zero. The resistance of wires 
made of alloys does not change so much with change of tem- 
perature as is the case with pure metals. The change 
in manganin wires for ordinary ranges of temperature is 
so slight as to be negligible. 

613. Conductance is the reciprocal of resistance. Thus a 
conductor whose resistance is one unit has a conductance of 
one unit. If the resistance is 3 ohms, the conductance is 
one- third of one unit, 1 etc. 

614. Conductivity is the reciprocal of resistivity. Silver 
has a low resistivity and a high conductivity. 

615. Resistance of Divided Circuits. Suppose three con- 
ductors to connect the points A and B, whose resistances 
are one, two, and three ohms, respectively. Then the 
conductance of the first is one 
unit, of the second \ unit, and of 
the third \ of a unit. The total 
conductance is therefore 1 + \ + 
\ = If units, and the resistance F , 
between A and B is the reciprocal 

of this number, 1 -=- If or -^ of an ohm. The fact that 
several parallel conductors offer less resistance than any one 
of them is what we should expect from the behavior of 
water, since water from a reservoir will flow more freely 
through several pipes than through one. 

616. The Unit of Electromotive Force and of Difference of 
Potential is the volt, named for Alessandro Volta (paragraph 
591). The exact definition of the volt is given in paragraph 
691. A Daniell cell or gravity cell with pure materials has 

1 There is as yet no agreement in regard to a name for the unit of 
conductance. Some writers have called it the mho. 





CONNECTION OF CELLS IN PARALLEL 297 

an E. M. F. of about 1.07 volts, and the various forms of 
Leclanche cell about 1.5 volts each. 

617. Cells Connected in Series. When a battery of several 
cells is made by connecting the copper of one cell to the zinc 
of the next, and so on, the cells are said to be connected 
in series. The E. M. F. of the battery is found by multi- 
plying the E. M. F. of one cell by the number of cells. In 
the arrangement shown in Fig. 307 suppose the E. M. F. 
of each cell to be 1 volt. The 

zinc of No. 2 is at the same 

potential as the copper of No. 

1, since they are connected by 

a good conductor. The copper 

of No. 2 is at a potential 1 

volt higher than its zinc. The Fig. 307.— Series connection. 

zinc of No. 3 is at the same 

potential as the zinc of No. 2, and so on. The difference 

of potential between the zinc of 1 and the copper of 3 is 

therefore 3 volts. Series connection is often illustrated by 

means of a series of pumps, each of which is capable of 

raising water to a certain height. A common pump will 

draw water from a well 25 feet deep. A second pump 

placed 25 feet above the ground would lift the water from the 

ground to that level, while a third 25 feet higher would raise 

it to a height 75 feet above the water in the well. 

618. Connection of Cells 
in Parallel. If several cells 
be connected as shown in 
Fig. 308 the E. M. F. will 
be the same as that of a 
single cell, since all the 
zincs are at the same poten- Fig. 308.— Parallel connection, 
tial and also all the coppers 

at the same, 1.07 volts higher than the zincs if they are grav- 
ity cells. This mode of connection corresponds to a group of 
pumps working side by side, pumping water from the same 
supply. They will raise the water no higher than one pump. 




298 CURRENT ELECTRICITY 

619. The Internal Resistance of a Battery of two cells in 
series is twice that of one cell, and is in general proportional 
to the number of like cells. If, however, the cells are con- 
nected in parallel, we have the same condition as with 
parallel conductors (paragraph 615). Two like cells offer 
half as much resistance as one, etc. 

620. Unit of Current Strength. The amount of water flow- 
ing through a pipe is measured by gallons per minute or 
cubic feet per second, or some other convenient units of 
volume and time. Current strength is measured in a single 
unit, the ampere, which is defined in paragraph 691. It is 
the amount of current which will deposit 1.174 grams of 
copper per hour from a solution of copper sulphate. A 
more satisfactory practical view of it is given by the state- 
ment that if the ends of a conductor whose resistance is 
one ohm have a difference of potential of 1 volt, a current 
of one ampere will flow through the conductor. 

621. Ohm's Law. The last sentence implies that the 
current in a circuit is directly proportional to the electromotive 
force and inversely to the resistance. This law was discovered 
by G. S. Ohm, a German scientist, about 1827. It is as 
true of any part of a circuit as of the whole. The amount 
of current flowing between any two points is directly pro- 
portional to their difference ,of potential and inversely to the 
resistance between them. 1 

622. Ohm's law is also conveniently expressed in the 

jp 
formula / = „, where / stands for current intensity, 

measured in amperes, E for electromotive force measured 

in volts, and R for resistance measured 

in ohms. Thus if the difference of poten- A~- 

tial of two electric light wires A and B 

is 110 volts and the resistance of a lamp B-* 

L connected between them is (when Fig. 309 

1 Of course this supposes that there is no battery or other source of 
E. M. F. between the points. 



5 




THE POWER OF CURRENTS 299 

hot) 220 ohms, one-half an ampere of current will flow 
through the lamp. 

623. Fall of Potential along a Wire. Suppose a uniform 
wire whose length is 4 meters and its resistance 2 ohms 
joins the points A and C, the potential 
of A being 1 volt higher than that of 
C. Half an ampere of current will flow 
through the wire. The resistance of 2 
meters of the wire will be one ohm. 
Let B be a point midway between A Fig. 310 

and C, and let the difference of poten- 
tial between A and B be X. Now the resistance of AB is 
1 ohm and the current flow is J ampere, so we have in the 
formula for Ohm's law / = %, R = 1, E = X. 

»-? 

X = -^ volt. 

Therefore the difference of potential between two points on 
the wire is proportional to their distance apart and to the 
resistance between them. 

624. We say in the case just cited that the potential falls 
\ volt between A and B, just as we say the level of the 
Niagara river falls 50 feet between the Whirlpool Rapids 
and Lake Ontario. The important fact that the fall of 
potential between any two points on a conductor through which 
current is flowing is proportional to the resistance between 
the points, from which it follows that the fall of potential 
along a uniform conductor is uniform, is thus seen to be 
another form of statement for Ohm's law. 

625. The Power of Currents is measured in watts (paragraph 
69). The rate at which a current of one ampere flowing 
under an E. M. F. of one volt can do work is one watt. An 
incandescent lamp carrying \ an ampere of current at 110 



300 CURRENT ELECTRICITY 

volts is using 55 watts of power. A street lamp carrying 
6.5 amperes, with, a difference of potential between its 
terminals of 70 volts, uses 455 watts. In measuring the 
power of large currents the kilowatt (1000 watts) is used. 
One kilowatt is nearly lj horse-power. 

626. The Amount of Heat Developed in a Conductor is 
directly proportional to the resistance, to the square of the 
intensity of the current, and to the time during which the current 
flows. When it is desired to produce heat or light by means 
of electricity, current may be sent through a conductor of 
high resistance. The trolley car is heated by a coil of 
resistance wire of some kind, and the filament of the in- 
candescent lamp is made of carbon, which is a very much 
poorer conductor than copper or other metals. Sometimes 
it is necessary to heat objects which are good conductors, 
as in the case of electric welding of railroad rails. Here 
the quantity of current must be made very high, thousands 
of amperes being used. 

627. In transmitting electric power over long lines, much 
of it will be lost as heat, radiated into the air by the con- 
ductors, unless the current intensity is kept very low or 
the conductors are made very large so as to keep down the 
resistance. The cost of large conductors is great, so that 
the other method of keeping down the heat loss is used 
wherever possible. If it is necessary to send 50 kilowatts 
over a long line, it may be done by sending only two amperes 
of current with an E. M. F. of 25,000 volts, or 100 amperes 
at 500 volts, or in any way so that the product of the 
number of amperes by the number of volts is 50,000. Two 
amperes can be sent with very small heat loss over a copper 
wire 1 mm. in diameter costing perhaps $5 per mile. To 
send 50 amperes with the same heat loss would require a 
wire 25 mm. in diameter, and costing 625 times as much. 
Since heat loss depends not at all on voltage, it is evident 
that it is more economical to send power in the form of 
high-tension currents. The disadvantage of very high volt- 
ages lies in the fact that they are dangerous, and cannot 



PROBLEMS AND EXERCISES 301 

safely be brought into buildings and used. The usual 
method of transforming them to lower voltages is men- 
tioned in paragraph 675. 



PROBLEMS AND EXERCISES. 

1. The copper of a gravity cell which had been in con- 
tinuous use for a week was found to have increased in weight 
25 grams. What has been the average current strength? 

2. Iron telegraph wires were taken down and replaced 
by copper wires of half the diameter. How will the resist- 
ance of the new line compare with that of the old one? 

3. At 0° C. the resistance of a copper telephone line is 
10 ohms. How much is it at 30° C? 

4. Two points are connected by five conductors. One 
of them has a resistance of 1 ohm, two 2 ohms each, and two 
3 ohms each. What is the total resistance between the 
points ? 

5. Three gravity cells connected in series send current 
through an external circuit whose resistance is 30 ohms. 
If the E. M. F. of each cell is 1 volt and its internal resistance 
5 ohms, what amount of current flows? 

6. With the same cells and external circuit, but the cells 
connected in parallel, how much current will flow? 

7. With the same 3 cells, and an external resistance of 
1 ohm, how much current would flow when the cells are 
connected in series? In parallel? 

8. On a telegraph line 30 miles long the resistance of the 
line wire is 15 ohms per mile. Five relays are in circuit 
whose resistance is 30 ohms each. The return is through 
earth, of which the resistance is negligible. How much 
current will 12 gravity cells in series, each having an E. M. F. 
of 1 volt and an internal resistance of 5 ohms, send through 
the circuit? 

9 Six gravity cells like those of Exercise 8 are arranged 
two in series and the three pairs in parallel (Fig. 311). How 
much current will they send through 5 ohms external 



302 



CURRENT ELECTRICITY 



resistance? How much through 10 ohms? Through 15 
ohms 





Fig. 311 



Fig. 312 



10. The same cells will send how much current through 
the same external circuits if they are arranged 3 in series and 
the two groups in parallel (Fig. 312)? 

11. Between two points whose difference of potential is 
110 volts, a lamp whose resistance is 220 ohms is connected 
in series with a wire whose resistance is 22 ohms. What is 
the difference of potential between the lamp terminals? 

12. On a certain circuit energy is lost in the form of heat 
at the rate of 1 kilowatt. What will be the rate of loss if 
twice as much current is sent over the circuit? 



MAGNETIC EFFECTS OF ELECTRIC CURRENTS. 

628. Magnetic Field about a Conductor. In 1819 Hans 
Christian Oersted, professor in the University of Copenhagen, 
discovered that when a current flows through a wire parallel 
to a suspended magnetic needle, the needle is deflected from 
its north and south direction. When Ampere 1 heard of 
Oersted's discovery he began a series of experiments which 
within a few days gave results leading to the very important 
generalization that a current-bearing conductor has a mag- 
netic field. 

629. Direction of Lines. In the case of a single straight 
cylindrical wire the lines of magnetic force are circles about 



1 Andre* Marie Ampere, 1775-1836. 
experimenter and thinker. 



French scientist. Brilliant 



MAGNETIC FIELD PROPORTIONAL TO CURRENT 303 




Fig. 313 



the wire. Fig. 313 shows a wire passing through the sheet 

of paper M N, carrying current in the direction shown by 

the arrow. A small compass needle such 

as was used in exploring the field about 

a magnet (page 263) will show that the 

lines of force are circles as shown. The 

arrows show the direction of the lines, i. e, 

the direction in which the north pole of 

the needle points as it follows around the 

circle. In general, to an eye looking along the conductor in 

the direction in which the current flows, the north pole of a magnet 

would rotate about the conductor in a clock-wise direction. 

630. If a wire carrying current be brought near to a com- 
pass needle, the needle tends to set itself at right angles to 
the direction of the current. The direction of swing of the 
north pole can be determined by the above rule. Another 
convenient rule is w 
illustrated in the dia- A S AJ 
gram. The magnet 
NS is pivoted, and 
the wire AB above 
the magnet is carry- 
ing current from A to B. The diagram shows the magnet 
and wire as seen from above. The right hand is placed near 
the wire, palm toward the magnet and fingers pointing in 
the direction of current flow. The north pole swings in the 
direction in which the extended thumb points. 

631. Magnetic Field Proportional to ^ 

Current. The strength of the mag- 
netic field due to a current is directly 
proportional to the strength of the 
current. The methods of current V ^ B 

measurement which are most used Fig. 315 

are based on this theorem. If a 

loop be made in a conducting wire so that it is carried twice 
past the same point, the magnetic field will be twice as 
strong as at a point which it passes only once. If the loop 




304 CURRENT ELECTRICITY 

in Fig. 315 is large and the current weak, the field is twice 
as strong at A as at B. By the use of a coil of wire, a 
feeble current may be made to produce considerable magnetic 
effects. 

632. Insulation. In order to cause the current to flow 
around all the turns of the coil, the wire is wrapped with 
cotton or silk thread or coated with other non-conducting 
material. Such wires are said to be insulated. 

633. Galvanoscope. In Fig. 316, in which a current flows 
over the needle from south to north and under it from 
north to south, the effect in deflecting the needle is twice as 
much as would be produced if the wire passed but once, 
since either wire acting alone would cause the north pole 
to swing toward the west. In general the needle tends to 
swing so as to bring the lines of its own field into a position 
parallel to those of the field due to the current. A coil 
of wire surrounding a pivoted magnetic needle affords a 



— r^ 




Fig. 316 Fig. 317.— Galvanoscope. 

convenient means for detecting the presence of current. 
Such a device is called a galvanoscope. This term is derived 
from the name of Galvani and is a reminder that electric 
currents were long called by many persons galvanic currents, 
and their phenomena were grouped under the head of 
galvanism. In Fig. 317 is shown a simple galvanoscope, 
the terminals of the coil being connected to the devices at 
A and B called binding posts, in which other wires may be 
conveniently clamped by thumb-screws. 

634. Galvanometers differ from galvanoscopes in having 
a scale or other device attached by which the amounts of 
current flowing through the instrument may be compared. 
Most galvanometers have a magnet and a coil. In some 



THE TANGENT GALVANOMETER 



305 



the magnet is free to move, and in others the magnet is heavy 
and fixed and the coil is light and free to move. 

635. The Tangent Galvanometer is shown in diagram in 
Fig. 318. A short magnet NS is suspended by a very thin 
fibre F at the centre of a circular conductor. The plane of 
this circle must be set in the magnetic meridian. When 
current passes around the coil in the direction shown by 
the arrow, the north pole swings west. 
The amount of deflection is read by 
means of a pointer fastened to the 
magnet and swinging over a scale 
graduated in degrees. The strength 
of the magnetic field due to the 
current is proportional to the current 
strength, but the angle of deflection is 
not proportional to it. The tangent 1 
of the angle of deflection is pro- 
portional to the strength of the magnetic field and therefore 
to the strength of the current flowing. Doubling the quantity 
of current does not give twice as great an angle of deflection, 
but an angle whose tangent is twice as great. The magnetic 
force called into being by the current is in this instrument 
pitted against the magnetic force of the earth's field. 




Fig. 318.— Tangent gal- 
vanometer. 



1 Fig. 319. — Tangent, as here used, is a 
trigonometrical term, but its meaning is 
easily defined. In the circle of the figure, 
let the angles AOB, AOC, etc., be 10°, 20°, 
30°, etc., AOH being 70°, AH being tangent 
to the circle at A. If the radius of the circle 
is 1 unit, the line AB, measured in the same 
unit, is numerically equal to the tangent of 
10°, AC to the tangent of 20°, etc. AOG is 
twice AOD, but its tangent AG is more than 
twice AD. 



20 




Fig 319 



306 



CURRENT ELECTRICITY 




Fig. 320.— Astatic 
needle. 



636. Astatic Needle. Where it is necessary to have a very- 
sensitive instrument a needle is sometimes used which is 
not affected by the earth. It is made by 
rigidly connecting two needles of equal 
magnetic strength, with their north poles 
pointing in opposite directions. The lower 
needle is then hung within the coil, and 
the upper one above it, as shown in the 
diagram, where F is the suspending fibre. 
The direction in which the compound 
needle points is controlled by the fibre, 
and if the suspension is made of a very 
slender fibre of silk that has never been 
twisted, the force required to deflect the needle will be very 
small, and when the current ceases to flow the elasticity of 
the silk brings the needle back to its previous position, parallel 
to the wires of the coil. Such a needle is said to be astatic. 

637. Moving Coil, or D'Arsonval Galvanometers are very 
much used. The plan of these instruments is shown in Fig. 
321. The coil C (which in practice has many 
turns of wire) is suspended by a very fine 
wire between the poles N, S, of a permanent 
magnet. Another slender wire connects one 
end of the coil to a support B, the other end 
being connected by the upper suspension to 
A. If a current is passed through the coil, it 
is made magnetic and swings around, tending 
to bring the lines of force of its field into 
parallelism with those of the permanent mag- 
net. The coil has no directive tendency when 
no current is passing, and the only force to be overcome in 
deflecting it is the elasticity of the metallic suspensions. 
M is a small mirror, used for the method of reading described 
in the next paragraph. Fig. 322 shows a standard form of 
D'Arsonval galvanometer. 

638. Telescope and Scale Readings. A much-used method 
of reading galvanometers is shown in Fig. 323. A small 




Fig. 321 



TELESCOPE AND SCALE READINGS 



307 



mirror M is attached to the movable coil (or needle). At 
a distance of half a meter or more from the mirror is placed 
a scale S\ and directly in 
front of the instrument 
the reading telescope T. 
The telescope is focussed. 
so that the middle point 
of the scale is seen re- 
flected by the mirror when 
no current is flowing. A 
vertical wire is so placed 
in the telescope as to be 
seen projected against the 
scale. ^ Tien a deflection 
occurs, some other point 
of the scale will be seen 

opposite the wire when FlG 322.— D'Arsonval galvanometer, 
the coil has come to rest. 





Reading 



Fig. 323 





Fig. 324. — D'Arsonval galvanometer, wall form. 



308 CURRENT ELECTRICITY 

When the deflections are small, the readings are almost exactly 
proportional to the current. The left-hand part of Fig. 323 
shows the field of view of the inverting telescope for two 
positions of the mirror. Fig. 324 shows a standard "wall 
form" of D'Arsonval instrument, with telescope and scale. 

639. Electromotive Force Measured by High-resistance Gal- 
vanometers. Suppose we wish to compare the E. M. F. of 
two batteries, whose internal resistances are two and five 
ohms, respectively. If we connect first one and then the 
other to a galvanometer whose resistance is 5000 ohms, 
and the deflections produced are the same, we conclude that 
the E. M. F. is the same in both cases. Let E = the number 
of volts in the E. M. F. of the first battery, and E' in that of 
the second. The whole resistance in circuit in the first 
case was 5000 ohms + 2 ohms = 5002 ohms, and in the second 
case 5005 ohms. By Ohm's law the current in the first 

E E' 

case was „.. rt and in the second ^7:7^. But because the 
5002 5005 

deflections were the same the amounts of current were the 

TP 7?' 

same. We have, then, — = —^ 

5005 E = 5002 E' 
E = .9994 E'. 
That is to say, E and E' are the same, or so nearly so that 
no ordinary measurement will show any difference. 

640. The Voltmeter is a high re- 
sistance galvanometer, whose sen- 
sitiveness is adapted to the E. M. F. 
to be measured, and which has a 
scale graduated so that readings 
may be made directly in volts. A 
simple form is shown in the dia- 
gram. NS is a magnet, pivoted 

so as to swing in a vertical plane. 
T , . t i ir • j u u • Fig. 325. — Voltmeter. 

It is enclosed on all sides by a hori- 
zontal coil of many turns of fine wire (shown cut off at CC so 
as to show the magnet). When current passes through the 




WATER ANALOGY FOR THE VOLTMETER 



309 



A 



coil the magnet swings, and the pointer shows on the scale 
the number of volts. This method of measuring electromotive 
force is not very accurate, since it assumes that all the other 
resistances in the circuit are so small as to be negligible in 
comparison with that of the galvanometer. 

641. Water Analogy for the Voltmeter. 
We may measure the height of a column 
of water by measuring the quantity of 
water that flows out of a very small open- 
ing at the bottom. Suppose A (Fig. 326) 
to be a vessel of water 10 meters high and 
1 meter square and C a very small open- 
ing. If 10 grams of water per second flow 
out of C, the amount flowing per second 
for a depth of 5 meters would be 5 grams ; 
for 3 meters depth, 3 grams per second, etc. 
If the vessel B is 10 cm. square for most 
of its height, the same jet attached to it 
would deliver 10 grams of water per second 
for a depth of 10 meters, although the 
resistance offered by the vessel B to the 
flow of the water is much greater than 
that of A . So nearly all the resistance is 
offered by the small opening C that the 
other resistances may be neglected in Fig. 326 
comparison with this. A tiny opening in 

a water-pipe alongside of a spigot measures by the flow of 
water from it the pressure in the pipe. When the spigot 
is opened the flow from the tiny leak is much less. 

642. A parallel case is observed in a trolley car on a line 
where only one or two cars run. When the incandescent 
lamps in the car are lighted, their brilliance decreases very 
much when the car is going up hill, because so much current 
is flowing through the motors that the E. M. F. is cut down 
and the lamps fade. On a city line where there are many cars 
and heavy currents flow, no such results are noticed. One 
car does not affect the E. M. F. So if our little leak were in 



310 



CURRENT ELECTRICITY 



a six-inch water pipe and the spigot one of ordinary size, 
the amount of water flowing from the leak would not be 
sensibly affected by opening the spigot. 

643. Amperemeters 1 are Galvanometers of very low Re- 
sistance, having scales reading directly in amperes. For 
laboratory use they are often made in the same form 
as the voltmeter of Fig. 325, having a coil of very few 
turns of very heavy wire. Where very heavy currents are 
to be measured they are often divided and a certain part 
only is sent through the instrument. 

The reason why the amperemeter must have very low 
resistance is easily seen if we refer again to our water analogy. 
In order to measure the water which flows through a certain 
pipe, a meter must be attached to it through which the 
water will flow with the least possible hindrance. 

If the strength of the earth's magnetic field is known, 
tangent galvanometers of low resistance may be used as 
current-measurers, but they do not usually read directly 
in amperes. 

644. Electro-magnets. The magnetic field about a coil 
carrying current may be greatly strengthened by placing 
inside the coil a core of iron, pref- 
erably as soft as possible. This 
effect is due to the great magnetic 
permeability of the iron (paragraph 
549), which causes the lines of force 
to crowd together in it instead of 
spreading through the surrounding 
space. The iron core and envelop- 
ing coil form what is called an elec- 
tro-magnet. Chiefly because soft 
iron has greater magnetic permeability than steel, it is possible 
to make electro-magnets stronger than permanent magnets. 
The greatest lifting power is obtained by making the core 
in the horses.hoe form and winding two coils, one about 



/F^ 




Fig. 327. — Cross-section 
of horseshoe electro-magnet 
with armature. 



1 Also called ammeters. 




THERMO-ELECTRIC COUPLE 311 

each pole. Approximately, the strength of the magnet is 
proportional to the number of ampere turns, that is, the 
product of the number of turns of wire in the coils by 
the number of amperes of current flowing. In order to 
make a very strong magnet we must also have a large 
core, for there is a limit to the number of lines of force 
which a given piece of iron can 
hold. When further increase of 
current does not increase the 
strength of the electro-magnet, the 
iron is saturated. 

645. To Determine the Poles of 
an Electro-magnet, a convenient 
method is to grasp it with the right 
hand, the fingers indicating the direction of current flow. 
The extended thumb will indicate the north pole. 

PROBLEMS. 

1. In order to reduce the sensitiveness of galvanometers, 
wires of low resistance are sometimes connected across 
the terminals, in parallel with the coil of the instrument. 
Such a wire is called a shunt. The coil of a galvanometer 
has 100 ohms resistance ; a shunt is put in whose resistance 
is 11-|- ohms. What fraction of the total current in the 
circuit passes through the instrument? 

2. The resistance of an amperemeter is .01 ohm. What 
must be the resistance of a shunt which permits ^ of the 
current to flow through the amperemeter? 

THERMAL CURRENTS. 

646. Thermo-electric Couple. If a piece of iron wire 
and a piece of copper wire be twisted together and 
their other ends attached to a sensitive galvanometer, 
and the junction of the two metals be then heated, the 
galvanometer will be deflected. Current continues to 



312 



CURRENT ELECTRICITY 



iron 



flow as long as the junction is hotter than the other parts 
of the circuit. The same result may be obtained with 
any two metals. The two 
whose thermal electro- 
motive force is highest 
are bismuth and anti- 
mony. 

647. Thermo-electric 
Generators. By joining 




Fig. 329. 




Fig. 330.— Plan of thermo- 
electric generator. 



Thermo-electric couple. 

many couples and heating alternate junctions, currents of 
considerable strength may be obtained. The plan of some 
such generators is shown in the 
diagram. Heat from a Bunsen 
burner or other convenient source 
is applied at the centre, and the 
other junctions project into the 
air in order to keep cool, for the 
E. M. F. depends on the difference 
of temperature of alternate junc- 
tions. Thermo-electric generators 
have not come into general use 
because the forms thus far de- 
vised are not durable. They have 
great interest because they afford the only known means 
of converting heat energy into electric energy directly. 

648. Thermo-pile. A large number of pairs of antimony 
and bismuth compactly mounted form, when connected to 
a sensitive galvanometer of low resistance, a very sensitive 
indicator of changes of temperature. Such a group is called 
a thermo-pile. 

INDUCED CURRENTS. 

649. Discovery of Induction of Currents. Joseph Henry 1 
made powerful electro-magnets within a few years after 

1 Joseph Henry, 1797-1878. Illustrious American physicist. First 
Secretary of the Smithsonian Institution. Teacher. Discovered the 
principles involved in the Electro-magnetic Telegraph. 



METHODS OF INDUCING CURRENTS 313 

Oersted's discovery, and both he and Michael Faraday 1 
reasoned that if magnets could be made by means of the 
electric current, it should be possible to produce electric 
currents by means of magnets. Both succeeded in obtain- 
ing magnetically induced currents independently of each 
other in 1831. Faraday's results were published first, 
and he is generally regarded as the discoverer of magneto- 
electric induction. The powerful currents employed for 
so many purposes in recent years are all produced by 
induction; so that we may call this discovery, the honor 
of which belongs jointly to Henry and Faraday, the begin- 
ning of the industrial applications of electric currents. 

650. Methods of Inducing Currents. Let C be a coil of 
wire of few turns, connected to a sensitive galvanometer, G, 
and NS a steel magnet. When the magnet is thrust into 
the coil, the needle of the galvanometer swings, but comes 
to rest in its previous position when the magnet lies still 
in the coil. When the magnet is withdrawn from the coil 
the needle swings in the opposite direction. Instead of 
a steel magnet we 
may use a current- 
bearing coil. Or if 
we let the second 
coil rest near the 
first and make and break the current through it, current is 
induced in the other coil. The circuit through which inter- 
mittent current is sent is called the primary circuit, and the 
other in which current is induced the secondary circuit. 
There are many other ways of inducing currents, but we 
may group them all by saying that current is induced in a 
circuit whenever the number of lines of magnetic force 
passing through it is changed. This law is often stated 



1 Michael Faraday, 1791-1867. Pupil of Humphry Davy. Lec- 
turer at the Royal Institution, London. Discoverer of the relation of 
magnetism to light. One of the most brilliant experimentalists that 
ever lived. 




Fig. 331. — Induction by a magnet. 



314 



CURRENT ELECTRICITY 




in a somewhat different form: current is induced in a 
circuit when the conductor making up any part of the circuit 
cuts the lines of force of a magnetic field. 

651. Direction of Induced Current. Lenz's Law. Sup- 
pose the magnet NS (Fig. 332) to be brought toward the 
electro-magnet AB, connected to the galvanoscope G. 
As the magnet approaches, it will induce a current in the 
direction indicated by the arrow. This current tends to 
make A a north pole. As NS is removed, 
current is induced in the opposite direction, 
tending to make A a south pole. In both 
cases the induced polarity in the electro- 
magnet tends to oppose the motion of the 
magnet. Always when current is induced by 
motion its direction is such as to produce a 
force tending to oppose the motion. This is 
Lenz's law. The law may be extended to 
the case where current is made and broken 
in a primary coil, by remembering that joining the circuit 
makes a magnet near the secondary, and the effect is the 
same as to bring near a magnet of the same polarity; 
while breaking the circuit has the same effect as the making 
away of a similar magnet. 

652. The Induction 
Coil. An arrangement 
by which intermittent 
currents are made to 
induce currents of al- 
ternating directionin a 
secondary coil is called 
an induction coil. The 
diagram shows the 
usual method of con- 
struction. Current 
from the battery B 

traverses the metal post A, the adjusting screw D, the metal 
spring E, and the inner coil wound on the iron core F, thus 




Fig. 333.— Induction coil. 



SELF-INDUCTION 315 

making F magnetic. The piece of iron / is attracted, draw- 
ing it away from the point of the screw D, thus breaking the 
circuit, demagnetizing the core, and releasing the piece of 
iron. The spring E throws / back against the screw, 
completing the circuit, and then the process is repeated. 
Thus the circuit is made and broken rapidly, and an equally 
rapid succession of momentary currents is induced in the 
secondary coil, which surrounds the primary, and whose 
terminals are marked + and — . When the current is 
made in the primary it induces in the secondary a current 
in the opposite direction (Lenz's law), and when it is 
broken it induces a current in its own direction. By 
winding very many more turns on the secondary than 
on the primary, an induced current of very high electro- 
motive force may be obtained. Large coils furnish cur- 
rents which will jump across an air space of many inches, 
forming brilliant and powerful sparks, similar in many 
respects to those of static electricity. 

The E. M. F. of the induced current made when the 
primary circuit is broken, whose direction is the same 
as that of the primary, is far higher than that of the reverse 
current. This is because the E. M. F. of the induced current 
depends on the rate of change in the strength of the magnetic 
field, and when the circuit is broken the magnetic field is 
destroyed almost instantly, while it does not reach its full 
strength so quickly when the circuit is closed. When the 
terminals are separated a considerable distance, current 
caused by the higher E. M. F. leaps across. The terminal 
from which it comes is called the + terminal of the coil, 
and the other the — terminal. C is a condenser, of many 
pairs of tinfoil plates, whose use is mentioned on page 316. 

653. Self-induction. When current is sent suddenly 
through a conductor it exerts an inductive influence on its 
own circuit, which, by Lenz's law, tends to oppose the cur- 
rent, and when the circuit is broken the inducing influence 
tends to cause a current in the same direction as that which 
has just been interrupted. If the break is very sudden, 



316 



CURRENT ELECTRICITY 



the self-induced current may have higher E. M. F. than the 
original current, and cause a spark to leap across the gap 
when the circuit is broken. A distinct shock may be felt 
from this " extra current/' as Faraday called it, if one 
hold in his hands wires from a battery of six or more cells 
and touch them together and then draw them quickly apart. 

654. Self-induction is much increased by winding a part 
of the circuit into a coil, because in such a case each turn of 
the coil exerts inductive influence on neighboring turns. 
Electrical gas-lighting devices consist of a circuit containing 
a " spark-coil" so arranged that a break is made above the 
burner when the gas is turned on, and the resulting spark 
lights the gas. In large induction coils sparking at the cir- 
cuit-breaking device, due to self-induction in the primary 
coil, would do damage, and is kept down by special devices, 
chiefly the use of condensers. Self-induction plays an im- 
portant part in the transformers used in connection with 
electric lighting by alternating currents. 

655. Earth Induction. If a few turns of wire be wound 
on a barrel hoop or a bicycle rim, and the extremities of this 
coil joined to the terminals of a sensitive galvanometer, 
current may be shown to be caused simply by turning the 
hoop over in the earth's field. 

656. Machines for Inducing Current work on the same 
principle as the first experiment described in paragraph 650. 
The diagram shows the arrangement of parts in the simple 
"magneto machine." N, 
S are poles of a perma- 
nent magnet. C is a coil 
of insulated wire called 
the armature wound on 
an iron core and mounted 
so as to revolve on an 
axle and cut the lines of force of .the magnet. One terminal 
of the coil is attached to the axle, which touches the spring 
B, and the other to the ring R, insulated from the axle. 
The spring B' touches this ring. From B and B' current 




Fig. 334 



THE COMMUTATOR 



317 



is led into the external circuit. D is a drive wheel, turned 
by any convenient source of power. During one-half of the 
revolution of the armature the current flows in one direction 
through the coil and external circuit, and during the other 
half in the opposite direction. 

657. The Commutator. For many purposes the alternating 
current is not satisfactory. It may be made to flow always 
in the same direction by the device called the commutator, 
shown in Fig. 335, which is a diagram of the end of the 
armature. CC is an end view of a single turn of the coil, the 
rest being omitted for the sake of clearness. One extremity 
of the coil is fastened to the half-cylinder of metal A, and 
the other end to A' '. Pieces of brass or copper, or sometimes 
of graphite, B, B' ', touch these half-cylinders as they revolve, 




UU 


\N\ 




B 


«o 


f^jf 




*\F 


\s 1 
n 

Fig. 335 


1* 1 
m 



the direction of revolution being shown by the arrows. 
In Fig. I current is flowing through the armature from 
A to A' ', and through the external circuit from B to B', B 
being the positive brush, and B' the negative brush. In II 
the conditions are the same except that the induced current 
is weaker, since the coil is not cutting so directly across 
the lines of force. In III the coil has begun to cut the lines 
of force in the opposite direction, so that current now flows 
from A' to A in the armature, but each brush is now in con- 
tact with the segment opposite to that touching it before, so. 



318 



CURRENT ELECTRICITY 




Fig. 336 



I 



that the current continues to flow from B to B' in the external 
circuit. 

658. Variation in Electromotive Force. The E. M. F. is 
proportional to the rate at which lines of force are cut. It 
is therefore greatest when the coil is in position I, since it is 
then in the strongest part 
of the field and is cutting 
across the direction of the 
lines most directly. When 
it is at right angles to posi- 
tion I it is moving along 
the lines of force instead 
of cutting them, and the 

E. M. F. is zero. If we represent the E. M. F. (and therefore 
also the intensity of the current, which varies as the E. M. F., 
the resistance being constant) by a curve in which the 
abscissas are times and the ordinates values of the E. M. F., 
we shall have for the alternating current such a curve 
as Fig. 336. From A to E 
is the time of a complete 
revolution. At A the wires 
of the armature are moving 
parallel to the lines of force 

of the field and the E. M. F. is zero. At B, after a quarter 
revolution, the E. M. F. is highest, at C again zero, and from 
C to D and on to E, negative because the direction of the 
current is reversed. The curve of Fig. 337 shows the E. M. F. 
for one and one-half revolutions of the armature with the 
commutator. The current from such a machine is called 
a direct or continuous current. 

659. Modes of Winding Armatures. The armature which 
we have been discussing, containing a single coil, is called a 
shuttle armature. Fig. 338 shows a cross-section of it, I 
being the iron core and C the coil wound lengthwise of it, 
as shown in Fig. 334. The disadvantage of such a machine 
is that it gives a current of widely varying intensity. By 
increasing the number of coils and correspondingly increasing 





Fig. 337 



THE DYNAMO 



319 



the number of commutator segments, one coil will be always 
in the strongest part of the field, and so the current intensity 





Fig. 338 



Fig. 339 




Fig. 340 



will be always high. The solid line in 
Fig. 339 shows the curve for an armature 
with two coils. By further increasing 
the number of coils, the current can be 
made nearly uniform. A cylindrical arma- 
ture with many coils is said to be drum- 
wound. Fig. 340 shows a cross-section 
of such an armature with six coils. 

The core of the armature is made of thin plates of iron 
with insulation between, to prevent induced currents in the 
iron, which would heat it and waste energy. The effect of 
these "eddy currents" may be illustrated by spinning a 
copper disk between the poles of an electro-magnet. It 
soon stops when the current is turned on, because its motion 
generates currents in itself; that is, it does work and uses 
up its kinetic energy. Another form sometimes used is the 
ring armature, in which the core is a ring of insulated iron 
wire, and the coil is wound continuously around it. Wires 
from many points in the coil are 
carried to the segments of the com- 
mutator. (See paragraph 686.) 

660. The Dynamo, or, to give it 
its full name, the dynamo-electric 
machine, differs from the magneto 
machine only in having its magnetic 
field created by an electro-magnet. 
Fig. 341 is a diagram showing the Fig. 341.— Series dynamo. 




320 



CURRENT ELECTRICITY 



plan of one form of dynamo. The armature A revolves 
between the poles, N, S, of an electro-magnet. The current 
induced in the armature is taken from the commutator C by 
the brush B' ', and led through the coils F of the electro- 
magnet, called the field-magnet, and then through the external 
circuit, represented by E, and back to the other brush B. 

661. How the Dynamo Starts. A piece of iron which has 
once been magnetized retains some magnetism. When 
the dynamo is started the armature revolves in a very 
weak magnetic field. The feeble current thus induced flows 
around the coils of the field-magnet and so strengthens the 
field. Now the induced current will be stronger, which in 
turn makes the field still stronger. This building-up pro- 
cess may go on until the field-magnet reaches saturation or 
until the limit of the driving power is reached. It will be 
noticed that Lenz's law operates in the case of the dynamo. 
A very small force suffices to start it, but the effect of 
the motion is to call into play a force tending to stop it, 
so that an armature which one could turn with one hand at 
the start may require a hundred horse-power engine to drive 
it when the machine has its "load." Such a machine as 
we have been considering is a series-wound dynamo, so called 
because the field coils are connected in series with the arma- 
ture and the external circuit. 

662. Shunt Winding. When there 
are two conductors between two 
points, one of them, usually that 
having the lower resistance, may 
be called a shunt. Thus when we 
wish to reduce the amount of cur- 
rent flowing through a galvanom- 
eter we put a shunt across its 
terminals. If the galvanometer has 
100 ohms resistance and the shunt 

10, the shunt will carry 10 times as much current as the gal- 
vanometer. In many instances it is not necessary to send all 
of the current around the field-magnet, and in such a case a 




Fig. 342. — Shunt dynamo. 



4 



/ 




1 / =* 




MULTIPOLAR DYNAMOS 



321 




Fig. 343. — Compound-wound 
dvnamo. 



shunt-wound dynamo may be used. In Fig. 342 the current 
divides at B, a part flowing through the lamps L and a part 
through the coils of the field-magnet. 

663. Compound Winding. Many dynamos are used to 
furnish continuous current for power and lights, where the 
quantity of current used varies very much from time to time. 
The form generally used in such 
a case is wound essentially as 
shown in the diagram. The cur- 
rent divides at C, a part going 
over the shunt coils F to B', and 
a part over the series coils R, and 
over the external circuit back to 
B'. If the machine starts when 
no current is being used, all that 
is produced goes over the shunt. 
As more and more current is 

used in the external circuit, the strength of the magnetic 
field is increased by the current flowing over the coils R, and 
if the coils are properly adjusted, a nearly constant difference 
of potential may be maintained between the brushes with 
a widely varying "load." 

664. Multipolar Dynamos. For many uses the dynamo 
with a two-pole field-magnet requires to be driven at high 
speed, making necessary a small wheel driven by a belt from 
a larger w^heel on the engine. In order 
to save space, directly connected engines 
and dynamos are desirable; that is, the 
armature is on the shaft turned by the 
connecting rod of the engine. But 
engines cannot economically run at such 
high speed as would be necessary for 
the armature of a dynamo, like Figs. 
342 and 343. In order to be run with 
slower speed of armature, and still obtain the necessary 
E. M. F., dynamos are built with many fields, or, better, many 
poles to the field-magnet. Fig. 344 shows the arrangement of 

21 




Fig. 344 



322 CURRENT ELECTRICITY 

the field of a six-pole machine. The armature has a modifica- 
tion of the drum winding. There must be as many brushes as 
there are poles, positive and negative brushes alternating. 
Such a machine and its field are shown on the opposite page. 

665. Alternators. For many purposes alternating currents 
are used. These are produced by means of a dynamo in 
which the armature coils are connected to rings instead of 
commutator segments. Such a machine cannot " excite" 
its own field, and a small continuous-current dynamo is 
used for this purpose. 

PRACTICAL APPLICATIONS OF ELECTRIC CURRENTS. 

666. The Kinds of Effects Produced by electric currents may 
be roughly classed under six heads : 

1. Chemical Effects. 

2. Heating Effects. 

3. Magnetic Effects. 

4. Physiological Effects. 

5. Production of Electro-magnetic Waves. 

6. Production of Kathode Rays and allied phenomena. 
We shall here consider only the first three of these classes. 

The last two are briefly considered in the next chapter. 

667. Electro-plating. The metals most used in electro- 
plating are copper, silver, and nickel. For laboratory experi- 
ments silver is the most satisfactory. A very good silver 
solution for the purpose is made from the double cyanide 
of silver and potassium. 1 Brass and copper objects receive 

1 To prepare the solution, dissolve a dime in as little nitric acid as 
convenient. Dilute the solution with water to about ^ pint. Add 
a strong solution of common salt, which will precipitate white silver 
chloride. After the chloride has settled for some hours, pour off as 
much of the blue liquid as possible and add as much water to wash 
the chloride. Let it settle again and filter or pour off the water. Add 
to the silver chloride slowly with continued stirring enough of a solution 
of 1 oz. potassium cyanide in 4 oz. of water to dissolve all the chloride. 
This substance must not be touched with the fingers or any part of the 
body. Great care must be taken not even to inhale the odor from it in any 
quantity. In common with all soluble cyanides it is desperately poisonous. 
When the chloride has been all dissolved the solution is ready for use. 




THE ELECTRIC ARC 323 

silver plating well. They must be very clean. It is well 
to use a little acid; dilute sulphuric is satisfactory. When 
the object to be plated is clean, wrap a bare copper wire 
loosely around it and hang it on the edge 
of a glass vessel as shown in the diagram. 
On the other side hang a silver coin, simi- 
larly supported. Remember that the solution 
is violently poisonous. Connect the zinc ter- ~j? IG 34 ^" 
minal of a cell to the object to be plated, 
and the copper or carbon terminal to the silver coin. In a 
few minutes the object will be coated with a firmly adherent 
film of silver. Rinse the object and the coin in a large vessel 
of water before touching them. 

668. The Electric Furnace is used in the manufacture of 
aluminum and some other metals, and for many other 
chemical processes. In one mode of making aluminum, 
carbon electrodes are immersed in a melted compound con- 
taining aluminum chloride. A very heavy current is passed 
through and the aluminum accumulates upon the negative 
electrode (the kathode). The E. M. F. required to decompose 
different compounds is very various. In the case of water 
it is about 1.7 volts, silver nitrate solution .7 volt, and zinc 
sulphate solution 2.4 volts. 

669. The Electric Arc. Sir Humphry Davy discovered, 
about the year 1800, that when two carbon points connected 
with the terminals of a powerful battery are brought together 
and then drawn a little distance apart, the current con- 
tinues to flow across the gap. It seems to be carried by the 
vapor of carbon and other substances present in the carbon 
which are vaporized by the intense heat. 1 This stream 
of vapor makes a sort of flame which is often somewhat 
curved; hence the name electric arc. The tips of the carbon 

1 It seems not unlikely that ionized air (see paragraph 707) between 
the carbons is a chief agent in conveying the current and that the bom- 
bardment of the 4- carbon by a stream of electrons (paragraph 703) is 
the cause of the intense heat. 



324 



CURRENT ELECTRICITY 



are highly heated, especially the positive one, and the carbon 
arc furnishes the most intense artificial light known. In 
the familiar street lamps 
a form now extensively 
used has pencils of gas 
carbon enclosed in a glass 
globe so as nearly to ex- 
clude the air. The carbons 
thus consume very slowly 
and require to be replaced 
only once a week instead of 
every day, as was the case 
with open arc lamps. 

670. Arc Lamps in Series. 
The customary arrange- 
ment of arc lamps for street 
lighting is in series. Seven 
amperes of current suffice 
to furnish a brilliant arc, 
and a current of about this 
strength is sent through the whole circuit. If the fall of 
potential between the carbons of each lamp is 75 volts, 
the power required to operate each lamp will be 7 X 75 = 
525 watts. If 40 lamps are in series the difference of poten- 
tial between the brushes of the dynamo will be 3000 volts. 




Fig. 346. — The electric arc. 



Fig. 347. — Arcs in series. 

In order to accomplish this, not only must the speed of the 
armature be high, but it must be wound with comparatively 
small wire, so that the rate of cutting lines of force may be 
high. This rate is the product of the number of lines of 
force by the number of wires crossing them per second. 

671. Incandescent Lamp. For house lighting and other 
uses where very intense illumination is not required, the 
" incandescent" lamp is extensively used. The word 



INCANDESCENT LAMPS 



325 




Fig. 348. — Incandescent 
lamp. 



itS3? = m 



incandescent means hot enough to shine. The light of the 
arc is due to incandescent carbon, but usage confines the 
term "incandescent lamp" to a glass 
globe from which the air had been 
exhausted, containing a carbon fila- 
ment whose ends are connected to 
two bits of wire melted into the glass. 
These wires are connected to two suit- 
able brass terminals, so that when 
the lamp is placed in its socket cur- 
rent flows through the carbon fila- 
ment, and because it is a bad conductor it is heated and 
shines. The carbon does not burn because there is no air 
in the globe to burn it. 

672. Incandescent Lamps are Ar- 
ranged in Parallel, as shown in the 
diagram, Fig. 349. When no lamps 
are turned on, no current flows 
through the external circuit. It is 
necessary to maintain a nearly con- 
stant difference of potential between 
the " leads" A and E, because the 
intensity of the light falls off very 
much with small fall in the E. M. F. 

This is because, unlike metals, the conductivity of carbon 
falls with decrease of temperature, so that the flow of cur- 
rent falls off much faster than the E. M. F. 

If a good conductor, such as a pin or a knife blade, is 
placed across the terminals to which a lamp should be at- 
tached, great damage might be done by the very heavy flow 
of current which would traverse the " short circuit." If 
the difference of potential is 110 volts and we put in a pin 
whose resistance is yj-g- of an ohm, we might expect a current 
of 11.000 amperes! Current enough to melt the wires and 
set things on fire would flow were these things not provided 
against by fuses somewhere in the circuit, which instantly 
rnelt out and stop the mischief. Suppose a six-inch water pipe 




326 



CURRENT ELECTRICITY 



passed through the kitchen. Water could be drawn out 
of it safely by a small spigot. What would happen if some 
careless person bored a four-inch hole 
in the pipe? That would be like stick- 
ing a pin through a lamp cord! 

673. The Nernst Lamp is an incandes- 
cent lamp in which the " glower" is not 
a carbon filament but a piece of a special 
sort of porcelain. It requires an alter- 
nating current, because if used with 
continuous current it is destroyed by 
electrolysis. 

Various other modifications of the 
incandescent lamp have been proposed. 
Some substitute other substances for 
carbon and some coat the carbon with a 
substance which increases its brilliancy. 

674. The Moore Light is made on the Fig. 350.— Short- 
plan of the aurora tube (paragraph 588). circuiting a lamp 
It employs an alternating current of high witn a P in > done 
voltage. Because of the large area from sometimes in pin- 
which the light comes it gives good illumi- ning on a shade> 
nation with small intrinsic brilliancy, and so is not trying to 
the eyes. 

675. Transformers. Where incandescent electric lights are 
used in rural neighborhoods at a long distance from the 
power station, high tension alternating currents are used. 
Since these are too dangerous to be 

brought into buildings, they must be 
" transformed" to lower voltage. This 
is done by means of an induction 
coil in which the primary current 
passes through many turns of small 
wire and the secondary coil is made 
of fewer turns of large wire. By this 
means a current is induced whose 
E. M. F. is lower than that of the Fig. 351. — Transformer. 




TELEGRAPH SOUNDER AND KEY 327 

inducing current. Such an induction coil is called a step- 
down transformer. In the diagram / is the laminated iron 
core, P the primary coil, and S the secondary. An ordi- 
nary type is one which steps down a 2200 volt current to 
110 for house lighting. 

676. Self-induction in the Transformer is so great when no 
current is being drawn from the secondary that very little 
current flows through the primary. The inducing force pulls 
all the time, but when there is no yielding no work is done. 

677. Step-up Transformers are used to give currents of 
very high voltage for long-distance transmission. In some 
instances they receive current from the dynamos at 2200 
volts and give out one at 22,000 volts. 

678. The Electro -magnetic Telegraph was invented by 
Samuel F. B. Morse, 1 although the principles involved 
were discovered by Joseph Henry. Henry had carried on 
extensive experiments with electro-magnets and had sent 
signals from one part to another of the buildings at Princeton, 
where he was teaching. The method used was the same 
as that now used in the telegraph " sounder." Morse saw 
the immense importance of the invention and devised the 
apparatus which was at first used in commercial telegraphy. 
He is also the author of the "Morse Code" of signals, still in 
general use. He secured the passage by Congress of a bill 
appropriating a sum of money to build an experimental 
line from Washington to Baltimore, which went into opera- 
tion in 1844. 

679. Telegraph Sounder and Key. The instrument now 
used for receiving telegraphic messages is the sounder, which 
consists of an electro-magnet and a lever carrying an iron 
armature A (Fig. 353). The lever is pivoted at P and a spring 
S holds it up against the screw B when no current is passing. 
When current is sent through the coil M (usually enclosed 
in a hard rubber case), the electro-magnet attracts the 

1 Samuel Finley Breese Morse (1791-1872). American portrait 
painter and inventor. 



328 



CURRENT ELECTRICITY 



armature and brings the lever down against the screw C, 
making a click. Of course the magnet may be made and 




Fig. 352. — Sounder and key. 

unmade by making and breaking the circuit at any point. 
This is done by a key, & simple form of which is shown in 



EJgiaB 




Fig. 353. — Diagram of sounder. 



-i^jt 



Fig. 354— Key. 



Fig. 354. When >the key is depressed, current flows, and 
when it is released the spring opens the circuit. 

680. Telegraph Line. The arrangement of a short tele- 
graph line is shown in Fig. 355. When no message is being 



K 

:C A 



S 



^ 




Earth 

Fig. 355. — Connections of a telegraph line. 



sent, switches M, M', attached to the keys K, K', are closed. 
The circuit is made up of the battery C, the instruments 



THE RELAY 329 

at the two stations, the line-wire L, and the earth. This 
does not mean that the same electricity which goes into the 
earth at A travels to B. The process of drawing current out 
of the earth at one end and discharging it into the earth 
at the other is like pumping water out of the sea at one end 
and discharging it through a long pipe into the sea at another 
point. When an operator wishes to send a message he 
opens the switch, and then when his key is depressed, current 
is sent over the wire and the sounder at the receiving station 
made to click. It is clear why the Daniell or some other 
form of non-polarizing cell must be used, since the current 
flows over the line practically all the time. 

681. The Morse Code consists of a set of signals made up 
of "dots" and "dashes." A dot is made by depressing the 
key and releasing if immediately, a dash by holding the key 
down a small fraction of a second. The following signals 
are those now in use: 

a b c d e f g 



m 



v w x y z period 

682. The Relay. In long lines the resistance of the wire is 
so great that the current is very feeble, and will not operate 
a sounder with sufficient force to give audible signals. The 

line current is sent through a 

relay, which is similar to the 

sounder, with itscoilshorizontal. 

The lever carrying the armature 

is thus vertical, that it may 7 ^B 

be withdrawn by a very weak circuit 

spring. The mass of lever and Fig. 356.— Plan of relay. 




330 



CURRENT ELECTRICITY 



armature is very small also, that they may more easily move. 
In the figure R is the magnet of the relay. The armature 
lever L is part of a " local circuit," as shown in the figure, 
including the battery B and the sounder S. When a sig- 
nal is sent over the line the lever L is attracted, touches the 
point P, closes the local circuit, and actuates the sounder 
S. Thus the feeble current delivers its message to the 
sounder to be interpreted, just as an exhausted courier might 
whisper his message in the ear of a herald. The principle 
of the relay was invented by Henry in 1836. 

In submarine telegraphy an insulated cable is used, and 
the receiving instrument is a galvanometer, of a form de- 
vised by Lord Kelvin 1 and called the " siphon recorder." 

683. Lifting Magnets are now extensively employed in 
loading and unloading iron and steel at foundries and 
rolling mills, and in moving heavy pieces about. The 
"travelling-crane" carries, instead of chains and hooks, 
an electro-magnet. This will take hold of the objects to 
be lifted simply by turning on the current, and let go by 
turning it off, thus saving time and labor in attaching and 
detaching chains and hooks. Much labor 
is saved in loading and unloading such 
material as pig iron and scrap iron. Many 
tons may be moved at once entirely with- 
out handling. 

684. The Electric Bell in its ordinary form 
is shown in diagram in Fig. 357. Current 
from L traverses the electro-magnet M, flows 
to the post P, through the spring S, the 
armature A, to the fixed screw B, and back 
to the source by U . The armature being 

attracted causes the bell, E, to be struck by the clapper. 
The circuit is broken at B; the clapper flies back and the 
process is repeated. 




Fig. 357.— Elec- 
tric bell. 



1 Sir William Thomson, Lord Kelvin (1824-1907). Great British 
scientist, mathematician, and inventor. See Frontispiece. 



ELECTRIC MOTORS 



331 



685. Electric Motors, now used for a multitude of purposes, 
are very various in design, but all those which use con- 
tinuous current are essentially the same as dynamos. Most 
direct current dynamos may be run as motors simply by 
sending current from another machine through them. The 
D'Arsonval galvanometer (paragraph 637) is a type of the 
electric motor, although because it has no commutator the 
coil will make only a half revolution. 

686. Perhaps the easiest form of motor to explain is that 
which has a ring armature (paragraph 659) and a two-pole 
field. Suppose current from any source to enter by the 
brush B. It divides at the point C, one-half traversing 
the coils CDF, and the other half the coils CEF, the parts 
joining at F and reaching the brush B' ', thence around the 





Fig. 358. — Diagram of Gramme ring motor 



Fig. 359 



field coils MM, and so back to the source. The current 
magnetizes the field as shown, and also magnetizes the 
armature, causing a south pole at S' and a north pole at N'. 
The poles of the field and of the armature attract each other, 
causing the armature to revolve. When the north pole of 
the armature has nearly reached the south pole of the field- 
magnet, the brushes slide on to the next commutator seg- 
ment, and so the poles are each shifted back one segment, 
the new poles are attracted as before, and the revolution 
continues. The arrangement of the lines of force, which 
always tend to shorten, is about as shown in Fig. 359. 



332 CURRENT ELECTRICITY 

Lenz's law applies to motors, as well as to dynamos. 
When the motor is running it tends to work as a dynamo, 
because it has a coil revolving in a magnetic field. This 
tendency sets up an E. M. F. opposite in direction to that 
of the driving current, and so causes a less amount of current 
to flow through the motor than we should expect from the 
resistance of the machine and the E. M. F. of the driving 
current. This back electromotive force does not act at first, 
because the machine is at rest, and if the full E. M. F. were 
turned on at once, too much current would flow, and the 
motor might be damaged. The starting box is a device to 
turn on the current gradually. 

687. Alternating Current Motors are in general not like 
dynamos. An important type uses a " two-phase" or " three- 
phase" alternating current, which on being passed through 
the field of the motor produces a rotating magnetic field. 
This rotating field induces currents in a rotating part not 
unlike an armature, but which has no connection with out- 
side circuits. The rotor, as it is called, rotates in consequence 
of the polarity due to its induced currents, which circulate 
entirely within itself. Such machines are called induction 
motors. Any satisfactory discussion of them and of the 
currents which operate them, would lead us beyond the limits 
of an elementary text, but this brief statement is inserted 
because of the great importance which such machines are 
assuming in this day of long-distance transmission of elec- 
tric power. 

688. The Telephone. Alexander Graham Bell invented, 
in 1876, the form of telephone which is now used as a receiver. 

Fig. 360.— Diagram of simple telephone line. 

It consisted of a steel magnet M, with a coil of fine wire 
wound about one pole, and a thin iron diaphragm D mounted 



THE CARBON TRANSMITTER 333 

near it_ Suppose a person talking at A. The diaphragm 
D vibrates in response to his voice. As it vibrates, it shifts 
some of the lines of magnetic force back and forth, and so 
generates alternating currents in the coil C. These are 
transmitted over the line wires L, L, to an exactly similar 
instrument at B, where they alternately strengthen and 
weaken the magnetism of M' and so cause its attraction 
for the diaphragm D' to vary. Thus the diaphragm at B 
vibrates in the same manner as that at A, and the sounds 
are reproduced. The sending instrument is a dynamo and 
the receiving instrument a motor! 

689. The Carbon Transmitter, due to Edison, 1 is now made 
in the form shown in Fig. 361. Coarsely ground gas carbon 
is contained in a cell of felt or similar material between the 
vibrating diaphragm A and the fixed plate C. The group 
of pieces of carbon is thus a part of the circuit including the 
battery B and the primary of the induction coil /. Pressure 
on the diaphragm pushes the pieces of carbon together and 




Fig. 361. — Arrangement of carbon transmitter. 

the resistance of the group is diminished. The current in 
the local circuit is thus strengthened, and current is thereby 
induced in the secondary of /. This current being of high 
E. M. F. traverses the line with small loss of energy and 
actuates the receivers. Modern receivers have horseshoe 
magnets with a coil about each pole. Telephones do not use 
earth return, as telegraph lines do, on account of the dis- 

x Thomas Alva Edison, distinguished American inventor (1847- — ). 



334 CURRENT ELECTRICITY 

turbances from stray currents and from currents induced in 
various ways, but have a complete metallic circuit. 

690. Telephone Signals are sent on long lines by high- 
voltage currents due to small magneto machines, which 
ring a special form of electric bell. The arrangements of 
switches, etc., on practical telephone lines are too various 
and complex to be discussed here. 

ELECTRICAL MEASUREMENTS. 

691. The C. G. S. System of Electro-magnetic Units. The 

unit of current in this system is the current which, flowing 
through one cm. of a circular conductor of one cm. radius, 
exerts a force of one dyne on a unit magnet pole at the 
centre of the circle. In making measurements of current 
the conductor actually consists of one or several whole circles 
of several centimeters radius. Since a radius of 10 cm. 
diminishes the force to yto °^ ^ na ^ a ^ one cm -> an( ^ a l en gth of 
62.83 cm. would give 62.83 as much effect as one cm. length, 
unit current flowing around a circular conductor of 10 cm. 
radius would exert .6283 of a dyne of force on a unit pole at 
the centre of the circle. The C. G. S. unit is equal to 10 
amperes. 

Unit quantity of electricity is the amount conveyed in one 
second past a given point by unit current. 

Unit difference of potential exists between two points when 
one erg of work is required to transfer one unit of + elec- 
tricity from the point of lower to that of higher potential. 
One volt equals 100,000,000 C. G. S. units. 

Unit resistance in the C. G. S. system is the resistance of 
a conductor in which unit current will flow when there is 
unit difference of potential between its ends. One ohm is 
equal to 1,000,000,000 of these units. 

692. Measurements of Electromotive Force and of Current in 
practical work are made with volt meters and amperemeters 
(sometimes called ammeters). More accurate methods are 
beyond the scope of this book. 



WHEATSTONE'S BRIDGE 



335 




Fig. 362 



693. Measurements of Resistance are made by comparing 
the unknown resistance with that of coils of wire whose 
resistance is known. Resistance coils are wound 
of doubled wire, as shown in the figure, in order 
to avoid self-induction (paragraph 654) and mag- 
netic effects. The material is German silver, 
manganin, or some other alloy of high resistance. 
Single coils may be mounted by inserting them 
in cylindrical blocks of wood and soldering the 

ends to heavy copper wires fastened in the block (Fig. 363). 

694. Wheatstone's 1 Bridge in some form is generally em- 
ployed in the measurement of resistance. The form shown 
in Fig. 364 is the " slide-wire", type, which is well adapted for 
laboratory work. More compact forms which can be used 
for measuring a wider range of resistances are employed in 
practice. At the ends of the bridge are heavy strips of brass 
or copper, AF and BN, between which is stretched over a 
meter-stick a piece of bare resistance wire, soldered to the 



h 



Fig. 363 




A ^ 2? 

Fig. 364. — Slide wire Wheatstone's bridge. 



copper strips at A. and B. OM is a heavy strip of copper 
having binding posts at 0, H, and M. Binding posts are 
also at E, F, N, and L. The resistance to be measured 
(x) is connected into the gap FO and a known coil, usually 
one ohm, in the gap MN. When the key K is depressed, a 
cell C sends current from L to E over two paths. One of 
these paths is the bridge wire BA and the other is made up 
of the two resistances, one ohm and x, and the copper strips, 



1 Sir Charles Wheatstone (1802-1875). Notable English scientist 
and inventor. His electric telegraph was long used in England. 



336 



CURRENT ELECTRICITY 



whose resistance is so small as to be negligible in comparison 
with the coils 1 and x. One terminal of the galvanometer 
G is connected to H, and the other is free to be placed at 
any point desired on the wire BA. When the current- is 
flowing we find by trial some point D on the bridge wire at 
which the free terminal of the galvanometer may be placed 
without causing any deflection. Now there is no difference 
of potential between D and H, or some current would flow 
when they are connected. That is, the fall of potential from 
L to D must equal that from L to H. Of course, the total 
fall from L to E is the same over both paths. Now the fall 
of potential along BA is uniform (paragraph 624) and along 
the other route the fall of potential all takes place in the coils, 
because the resistance of the copper strips is so small. Sup- 
pose D to be 40 cm. from B and 60 cm. from A. Now since 
fall of potential is proportional to resistance (paragraph 624), 
we have the proportion: 

BD : DA : : 1 ohm : x 

or 40 : 60 : : 1 : x 

whence x = 1\ ohms. 
Because of lack of uniformity in the wire, the results may be 
slightly in error. This may be avoided by reversing the coils 
and repeating and then taking a mean of the two results. 

695. Comparison of Wheatstone Bridge with the Balance. 
The form of Wheatstone bridge just described is like a 
balance in which the unknown 
weight is hung on one end and 
1 kg. on the other, and the ful- 
crum moved until it balances. 
Then, disregarding the weight of 
the lever, we should find x by a 
simple proportion. In this case the distances are inversely 
proportional to the weights, while in that of the bridge they 
are directly proportional to the resistances. 

If the contact D (Fig. 364) were fixed at the middle of 
AB, and we added resistances at MN until no deflection 
occurred, the resistance at x would equal those at MN, 



40 



-zs: 



60 



®-l* 







Fig. 365 



STATIC AND CURRENT ELECTRICITY 337 

just as in the balance of equal arms the weights in one pan 
equal the weight of the object in the other. Practical instru- 
ments are made on this plan, providing a set of coils for com- 
parison, corresponding to a set of weights for weighing. 
They also have means for setting the balance arms at the 
ratios 10 : 1, 100 : 1, 1 : 10, etc., as well as 1 : 1. Thus 
a vast range of resistances may be measured with a single 
instrument. 

696. Comparison of Static and Current Electricity. The water 
analogy which is so helpful in the case of current electricity 
in helping us to connect the facts and picture their relations 
to each other furnishes little aid to an understanding of the 
phenomena of static electricity. The differences of potential 
with which we deal in the case of static electricity would be 
reckoned in millions of volts. If we compare the flow of 
electricity at a potential difference of one volt to water 
flow with a difference of level of one inch, a house current of 
110 volts would be comparable to /^T\ 

water flowing between levels nearly yi \Q) 

10 feet apart. On the same scale, p, / [^ 

the water pressure which we must \f / \ 

use to picture electrostatic differences i <_ + * '^£ —^-> 1 ^E 
of potential would have to be reck- ~ ] 

oned in miles. In laboratory ex- IG * 

periments the quantity of electricity which flows when an 
electrostatic discharge takes place is infinitesimally small 
reckoned in amperes. 

The identity of the two kinds is shown by a beautiful 
experiment with the electrophorus. The discharge of any 
charged body involves electric flow; that is, an electric 
current, but commonly a discharge is so sudden that if it is 
sent through a galvanometer no effect is produced because 
the moving parts have too much inertia to be set in motion 
by current lasting such a short time. If the lid of the 
electrophorus be connected with one terminal of a sensitive 
galvanometer, and the other terminal connected with the 
earth or held in the hand, when the lid is slowly lifted from 
22 



338 CURRENT ELECTRICITY 

the excited shellac plate the galvanometer is deflected, and 
when it is replaced the galvanometer swings in the other 
direction. When the lid is lifted the positive charge slowly 
flows to earth through the galvanometer by the wire E 
(Fig. 366), and when it is returned current flows in the other 
direction 



PROBLEMS AND EXERCISES. 

1. Why does increasing the number of turns on the 
secondary of an induction coil increase the E. M. F. of the 
induced current? 

2. If the magnet of a tangent galvanometer is suspended 
over a copper plate it comes to rest after being set to swinging 
much more quickly than if the copper plate is absent. Why 
is this? (Paragraph 659.) 

3. Why is it not necessary to build up laminated cores for 
field-magnets, as it is for armatures ? 

4. D'Arsonval galvanometers often have a soft iron core 
between the poles of the magnet, the coil swinging between 
the magnet and the core. What advantage does the core 
give? 

5. One Daniell cell will not electrolyze water. Two or 
any larger number in series will. Why is this? (Para- 
graph 668.) 

6. In measuring a resistance with a slide-wire bridge, 
the point of no deflection was at 48.3 cm. with the bridge 
arranged as in Fig. 364. Calculate the resistance of the 
unknown coil. Reversing the positions of the one ohm 
coil and the unknown, the point of no deflection was 51.5. 
Calculate the value of x in this case. Why are the values 
not the same? 

Note. — An excellent book for the student who wishes 
to pursue the subject of electricity and magnetism, is 
Silvanus P. Thompson's Elementary Lessons in Electricity 
and Magnetism, Macmillan & Co. 



CHAPTEE XII. 
ELECTRO-MAGNETIC WAVES AND RADIO-ACTIVITY 

ELECTRO-MAGNETIC WAVES. 

697. The Ether. We speak with confidence of the exist- 
ence of the ether, although we know literally nothing of its 
nature and properties, because we find that many of the 
phenomena of light, heat, and electricity cannot be accounted 
for without supposing the existence of a medium which fills 
space. If we suppose it to be a gas, we must assign to it a 
very high molecular velocity, since it is not controlled by the 
gravitation of the earth or even of the sun, but extends 
throughout space. The fact that some kind of periodic 
disturbance of this ether takes place, in other words that 
there are light waves and heat waves has been known for a 
century. 

698. Maxwell's Electro -magnetic Theory. About 1867 Max- 
well 1 showed mathematically that light and heat must be 
electro-magnetic disturbances. While his reasoning is con- 
vincing, it does not appeal to the majority of people, 
because of the difficulty of the mathematics involved. 

699. Electro -magnetic Waves were finally produced in 1887, 
and found to behave like light waves in that they can be 
reflected, refracted, and diffracted, and that their speed 
is that of light. This discovery is due to Hertz. 2 The 
waves were made by sparks from an induction coil, passing 
between small metallic spheres. That is to say, a rhythmic 

1 James Clerk Maxwell (1831-1879). Great English mathematician 
and physicist. 

2 Heinrich Hertz (1857-1894). German scientist. 

(339) 



340 ELECTRO-MAGNETIC WAVES AND RADIO-ACTIVITY 



electric discharge sends waves through the ether just as 
rhythmic motion of a tuning fork prong sends waves through 
the air. Hertz detected the waves by means of a hoop of 
metal with a very small gap. When this hoop was placed 
in the path of the waves, electric oscillations were set up in 
it which produced a spark across the gap. The loop behaved 
in much the same way as a tuning fork which is set in vibra- 
tion by a succession of small impulses correctly timed. 

700. The Coherer. Hertz waves could not be detected by 
the means just described except at points near their origin. 
Edouard Branly, a Frenchman, discovered that a group of 
loose filings of silver or nickel subjected to the action of 
electric waves becomes a conductor of electricity. The filings 
are put in a small glass tube between two metal plugs which 
are the terminals of a circuit including a battery and relay. 
The tube with its filings and 
plugs is called a coherer. In 
order to increase the sensi- 
tiveness of the coherer to 
electro-magnetic waves, one 
end of it is connected to 
earth by a wire, and the 
other to a long wire extend- 
ing up into the air, called 
an antenna. When a train 
of waves strike the antenna 
M, electrical vibrations are set up in it, which so affect the 
filings as to cause them to "cohere" and become conducting. 
Current then flows from the battery B through the relay R. 
The armature A is attracted, the circuit of the battery B' is 
closed, and the sounder clicks. The coherer is placed near 
the sounder, so that the blow of the lever shall disturb the 
filings and cause them to decohere and so be ready to receive 
another signal. 

701. Wireless Telegraphy is carried on by means of a re- 
ceiving apparatus such as has been described, and a sending 
instrument consisting of a powerful induction coil provided 




Fig. 367. — Wireless telegraph re- 
ceiving station. Size of coherer 
much exaggerated. 




KATHODE RAYS 341 

with an antenna attached to one terminal and a ground con- 
nection attached to the other. The current in the primary 
of the coil is made and broken by means of a key as in ordi- 
nary telegraphy. A "dot" is a short succession of sparks 
from the secondary, caused by depressing the key and 
releasing it at once. Thus a short train of waves is sent 
through the ether in all direc- 
tions from the antenna . Dashes 
are made in a corresponding 
manner, and so messages are 
sent with the ordinary Morse 
code. Instead of the coherer 
Marconi 1 now uses another re- 
ceiver, shown in diagram in ^ oao J, ., 
_. ' & . Fig. 368 — Marconi's receiver. 

Fig. 368. An antenna A, con- 
nects with a coil C, whose other terminal is connected to 
earth by the wire E. An outer coil wound about C is con* 
nected to the telephone receiver R. A core of iron wires / 
in the form of an endless rope passes with uniform speed 
through the coil. M, M are horseshoe magnets. Ether 
waves send pulsations up and down the line from A to E, 
and the induced currents in the outer coil cause sounds in 
the telephone receiver. 

The chief value of wireless telegraphy at present is for 
maintaining communication with ships at sea. Trans- 
atlantic messages were first sent commercially in 1907. 

RADIO-ACTIVITY AND OTHER RECENTLY DISCOVERED 
FORMS OF RADIATION. 

702. Kathode Rays. The fact has been mentioned (para- 
graph 588) that electricity flows through a tube from which 
the air has been partly exhausted. If the exhaustion be 
carried far enough no flow takes place. If the terminals of 
an induction coil are attached to a tube in which the vacuum 

1 Chevalier Guglielmo Marconi, Italian inventor (1875 ), notable 

for his work in rendering wireless telegraphy a practical success. 



342 ELECTRO-MAGNETIC WAVES AND RADIO-ACTIVITY 

is as high as one-thousandth of a millimeter a stream of 
particles is repelled from the negative electrode (kathode). 
These streams, called kathode rays, excite fluorescence of 
the glass against which they strike. That is to say, they 





Kathode rays. Concentration of rays. 

Fig. 369 

render the glass luminous. If the kathode is made of a 
concave piece of metal, the rays are concentrated at the 
centre of curvature, and an object placed there may be very 
highly heated. 

703. The kathode rays were extensively investigated about 
1875 by Crookes, 1 and the tubes were called Crookes' tubes. 
The rays are attracted by a magnet and repelled by a 
negatively electrified body, and must therefore consist of 
negatively charged particles. The mass of these particles has 
been calculated by J. J. Thomson 2 and others from the size of 
the electric Charge which they carry, and found to be in the 
neighborhood of one-thousandth of the mass of a hydrogen 
atom. The name electrons is now given to these exceedingly 
minute charged particles, which are believed to be split off 
from the gaseous molecules. 

704. Rontgen Rays. When the kathode rays strike against 
the surface of the enclosing glass they cause another form 
of radiation to be given out from the glass. These rays, 
first observed in 1895 and called from their discoverer 

1 Sir William Crookes (1832 ). Celebrated English physicist, 

chemist and psychologist. 

2 Joseph John Thomson (1856 ). Brilliant English physicist. One 

of the foremost investigators in electricity and allied fields. 




IONIZATION OF GASES 343 

Rontgen 1 rays, are not deflected by the magnet, are not 
refracted nor reflected, and no interference phenomena have 
been observed in connection with them. They are now 
supposed to consist of irregular disturbances in the ether, 
propagated like light 
waves but differing in 
their behavior because 
they are not rhythmic. 
Because of the uncer- 
tainty in regard to /£ 
their nature Rontgen Fig, 370.— X-ray tube, 
called them " X-rays," 

and this is the name by which they are commonly known. 
The form of tube generally used to generate them is shown 
in its essential features in Fig. 370. Kathode rays are con- 
centrated on the piece of platinum P, which thus becomes 
the source of the Rontgen rays. They pass through the glass 
of the tube, while the kathode rays do not. 

705. Rontgen rays act on a photographic plate as light 
does. They render certain substances fluorescent. They 
penetrate such substances as paper, wood, and flesh quite 
easily. Facing page 342 is a " radiograph" of a foot with the 
shoe on taken with these rays, by placing the foot on a pho- 
tographic plate enclosed in a black paper envelope and 
then exposing the whole to Rontgen rays. Bones are 
much more opaque to this radiation than flesh, and the 
denser metals are quite opaque to it. 

706. Surgeons use Rontgen rays in examining broken 
bones and in locating foreign objects which have entered 
the body. They are also used in the treatment of skin cancer 
and some other diseases. Intense or long-continued action 
on the skin produces painful injuries much like burns. 

707. Ionization of Gases. One of the most curious results 
of Rontgen rays is that they render the gases through which 

1 Wilhelm Konrad Rontgen (1845 ). Distinguished German 

physicist. 



344 ELECTRO-MAGNETIC WAVES AND RADIO-ACTIVITY 

they pass electrically conducting, so that the charge of an 
electrified body surrounded by the gas is quickly dissipated. 
It seems that the radiation disturbs the gaseous molecules 
in such fashion as to cause electrons to split off from them, 
and these electrons discharge the electrified body. The 
gas under these circumstances is said to be ionized, and 
is to some extent a conductor of electricity. We may, if 
we choose, say that the gas conducts away the charge of 
the electrified body. The term ionization is from the word 
ion which is the name given to the parts into which the 
gaseous molecules or atoms split up. The negative ions 
are identical with electrons, and are the same, from what- 
ever gas they are produced. 

708. Rise of temperature also has a tendency to ionize 
gases, and this probably accounts for the fact that experi- 
ments in static electricity succeed best in cold weather. 
The ions of gases gradually recombine when the gas is free 
from disturbing causes. 

709. Becquerel Rays. In 1896 Becquerel 1 discovered that 
salts of uranium, when near a photographic plate, send 
out a kind of rays which affect the plate. Another investi- 
gator soon afterward found that thorium 2 compounds do the 
same thing. These radiations have the power to produce 
fluorescence, to discharge electrified bodies (i. e., to render 
gases conducting), and to penetrate many opaque sub- 
stances. They are deflected, as are the kathode rays, by a 
magnet or by an electric charge. From their discoverer, 
these are called Becquerel rays. 

710. Radium. Soon after the discovery of the Becquerel 
rays, Madame Curie 3 examined all the known elements in 

1 Antoine Henri Becquerel (1852 ). French physicist. His father 

and grandfather were noted scientists. 

2 Thorium is the element whose oxide is the chief constituent of 
Welsbach light "mantles." 

3 Pierre Curie, born in Paris, 1859, and his wife, Marie Sklodowska 
Curie, born in Warsaw, 1867, achieved world-wide fame as the dis- 
coverers of radium (1903). Prof. Curie was killed in a street accident 
in 1906. 



NATURE OF THE EMANATION 345 

the search for other sources of rays similar to those given 
out by uranium and thorium. These two metals, because of 
the property of sending out this new form of radiation, are 
called radio-active substances. None of the other elements 
then known were found to have the property to any con- 
siderable extent, but pitch-blende, an ore of uranium, was 
found to be four times as radio-active as uranium itself. 
Concluding that pitch-blende must contain some unknown 
element more radio-active than uranium, she and her husband 
subjected pitch-blende to a most exhaustive and ingenious 
analysis, and were rewarded by the discovery of several 
new elements, all of which are radio-active. The most 
remarkable of these is radium. The amount of labor and 
skill involved may be imagined from the fact that a carload 
of the mineral had to be worked over to get half a gram of 
radium, which proved to be several hundred thousand times 
as radio-active as uranium. The activity of radium com- 
pounds is so great that a glass tube containing a few milli- 
grams of the bromide which a man carried in his vest pocket 
for a half day made a painful burn on his skin ! 

711. The Nature of the Particles Emitted has been investi- 
gated by Rutherford, 1 who separated the rays by passing 
them through an electric field. He found that the radiation 
was by this means separated into three parts, one of which 
is attracted by a negatively charged body, one is repelled, 
and one is not affected. These three streams he named 
respectively alpha, beta, and gamma rays. The beta rays 
behave in every respect like kathode rays, that is, like 
streams of electrons. The particles of alpha rays have 
greater mass, less velocity, and less penetrating power 
than those of the beta rays, and correspond to the positive 
ions of ionized gases. The gamma rays have great pene- 
trating power and seem to be like Rontgen rays. 

1 Ernest Rutherford, born in 1871, in New Zealand. Professor of 
Physics at McGill University, Montreal, 1898-1907. Now (1908) pro- 
fessor in Manchester University, England. 



346 ELECTRO-MAGNETIC WAVES AND RADIO-ACTIVITY 

712. Ramsay 1 seems to have shown (1903) that a part of 
the emanation from radium becomes helium, the wonderful 
gas named before its discovery on the earth from the fact 
that a line of its spectrum was observed in the spectrum of 
the sun (paragraph 415). More recently Ramsay, having 
subjected a compound of copper to the action of radium, 
seems to have shown that a very minute part of the copper 
was converted into lithium, the lightest known metal. 

713. Radio-active Substances are Decomposing. This con- 
clusion seems to be a fair inference from the facts. The 
decomposition must, however, be exceedingly slow, since no 
sample of radium has yet been observed to diminish in weight, 
although some have now been under observation for five 
years. The most marvellous thing about radium is the fact 
that it continually gives out energy in the process of decom- 
position. The bombardment to which radium is subjected 
by the escaping particles raises its temperature. A mass of 
radium gives out every hour heat enough to melt its own 
weight of ice. Such facts as these give us a new conception 
of the amount of energy which may be stored in a small 
space! 

714. The discoveries since 1896, in the field of radio-activ- 
ity have revolutionized our ideas of the constitution of matter. 
It is certain that atoms are not indivisible. It seems to 
have been proved that some at least of the elements are not 
permanent, and that the atoms, at least the heavier 2 ones, 
hold stored up within themselves vast quantities of energy. 

Theories and speculations in regard to the facts of radio- 
activity are abundant, but it is scarce worth while to record 
here anything but what seem to be facts, since a theory 
credited today may be discredited tomorrow. 

1 Sir William Ramsay, born in Scotland in 1852. Discoverer (jointly 
with Lord Rayleigh) of argon and helium. Perhaps the most celebrated 
living chemist. 

2 The atomic weights of uranium, radium, and thorium are the three 
highest known. 



INDEX. 

(Numbers refer to pages.) 



Absolute zero, 24 
Acceleration (def.), 23 

due to gravity, 42 

variable, 121 
Achromatic lens, 208 

prism, 201 
Air, composition of, 100 

-pump, 112 

-waves, 131 
Alternating currents, 317, 322 

motors, 332 
Altitude determined by barometer 

(table), 108 
Amperemeter, 310 
Aneroid barometer, 108 
Anode, 289 

Applications of electricity, 322 
Arc, electric, 323 
Archimedes, 82 
Armatures, 318 
Astigmatism, 193 
Atmosphere, 99 

pressure of, 102 
Atmospheric electricity, 283 
Aurora Borealis, 285 



Balloons, 101 
Barometer, 106 

aneroid, 108 
Batter v, 288 

storage, 292 
Beats, 155 
Bellows, 118 
Binocular vision, 197 
Blower, 118 
Bodv (def.), 10 
Boiling, 239 
Boyle's law, 108 



British thermal unit, 229 
Brittle (def.), 17 
Buoyancy, 78 
of air, 101 



Calorie, 229 
Camera, 191 
Candle power, 174 
Capillarity, 71 
Cartesian diver, 118 
Caustic of reflection, 182 
Cells, bichromate, 291 

Bunsen, 291 

connection of, 297 

Daniell, 290 

dry, 292 

energy transformation in, 293 

Grove, 291 

simple, 287 

single fluid, 291 

storage, 292 
Centre of gravity, 32 
Centrifugal force, 39 
Change of state, 232 
Charge, electric, 272 

unit, 275 
Charles' law, 226 
Chemistry (def.), 9 
Chladni's figures, 158 
Chromatic aberration, 207 
Circuit, electric, 288 
Clouds, 238 
Coefficient of linear expansion, 223 

of cubical expansion, 225 

of friction, 48 
Coherer, 340 
Color, 199 

-blindness, 212 



(347) 



348 



INDEX 



Color of opaque objects, 210 

-sense, 211 
Commutator, 317 
Compass, 264 

Compensating pendulum, 224 
Complementary colors, 209 
Composition of displacements, 22 

of forces, 26 

of velocities, 21 
Concave mirrors, 178 
Concurrent forces, 26 
Condenser, electric, 279 
Conductance, 296 
Conduction of heat, 247 

of electricity, 271 
Conductivity, 296 
Conjugate foci of mirrors, 179 

of lenses, 189 
Conservation of energy, 40 
Constancy of Nature, 11 
Convection of heat, 248 
Convex mirrors, 181 
Cooling by evaporation, 239 

by expansion, 244 
Cord, 63 

Coulomb's law, 275 
Couple, 32 
Critical angle, 185 

temperature, 244 
Current electricity, 286 

strength, 298 
Curvature of the earth, 69 
Cylindrical mirrors, 181 



Declination, magnetic, 265 
Density (def.), 14 

of gases (table), 101 

of liquids, 85 

of stone, 83 

of water, greatest, 234 

of wood, 84 
Dew-point, 237 
Diatonic scale, 161 
Diffraction, 214 
Diffusion of gases, 99 

of light, 175 
Dimension (def.), 12 
Dip, magnetic, 266 
Discord, 164 
Dispersion, 199 



Distillation, 242 
Distribution of heat, 246 
Doppler's principle, 147 
Drops, 70 
Ductility, 17 
Dynamo, 319-322 
Dyne, 25 



Ear, 160 

-trumpet, 141 
Earth a magnet, 263 
Efficiency of machines, 63 
Elasticity, 16 

of liquids, 73 
Electric arc, 323 

bell, 330 

furnace, 323 

motors, 331 

attraction and repulsion, 271 
Electricity, static, 270 

current, 286 
Electrode, 289 
Electrolysis, 289 
Electrolyte, 289 
Electro-magnet, 310 
Electro-magnetic waves, 339 
Electromotive force, 286 

unit of, 296 
Electrons, 342 
Electrophorus, 277 
Electro-plating, 322 
Electroscope, 274 
Energy, 36 

conservation of, 40 

formulse for, 51 
Equilibrium of bodies, 32 

of floating bodies, 80 

of forces, 28 
Erg, 36 
Ether, 167, 339 

waves, 136 
Evaporation, 237 
Expansion by heat, 222 
Experiment (def.), 11 
Extension, 12 
Eye, 192 



Falling bodies, 41 
Fall of potential, 299 



INDEX 



349 



Far-sightedness, 193 

Field glass, 195 

Filter pump, 115 

Flexibility, 18 

Floating bodies, 79 

Flying, 110 

Force (def.), 10 
centrifugal, 39 
measurement of, 24 

Forced vibrations, 151 

Franklin's experiment, 283 

Freezing point, 233 
mixture, 235 

Friction, 47 

Fusion, 232 



Galileo, 41 
Galvani, 286 
Galvanometer, 304-308 
Galvanoscope, 304 
Gas and gasoline engines, "256 
Gases, 98 

Graphic representation of forces, 
25 
of velocities, 21 
Grating, diffraction, 214 
Gravitation, law of, 13 
Greenhouses, 251 



Hardness, 17 
Harmonic curves, 124 

motion, 122 

composition of, 124 
Heat, 218 

developed by electric currents, 
300 

engines, 252 
Heating by hot water, 249 

by steam, 249 
Hooke's law, 16 
Horse-power, 40 
Hvdraulic ram, 94 

lift, 96 
Hydrometer, 86 
Hydrostatic press, 74 



Ice machines, 245 
Impulsive forces, 27 



Incandescent lamps, 324 
Inclined plane, 60 
Indestructibility of matter, 15 
Index of refraction, 184 
Induced currents, 312 

electrification, 274 
Induction coil, 314 

earth, 316 
Inertia, 15 

moment of, 38 
Influence electrical machines, 278 
Insulation, 304 
Insulator, electric, 304 
Intensity of sound, 148 
Interference of light, 212 
of sound, 148 
of waves, 135 
Interval, musical, 161 
Ionization of gases, 343 



Kathode, 289 
rays, 341 

Keynote, 163 

Kinetic energy, 37 
theory of gases, 98 
theory of liquids, 68 

Konig, 149 



Latent heat, 233 
Law, Boyle's, 109 

of Charles, 226 

Coulomb's, 275 

of friction, 48 

of gravitation, 13 

of the inclined plane, 61 

Lenz's, 314 

of the lever, 57 

of machines, 63 

of magnetic action, 260 

of motion, 24, 27, 28 

Ohm's, 298 

of the pendulum, 53 

of the pulley, 59 

of the screw, 62 

of vibrating strings, 157 
Lenses, 188 
Lever, 56 
Levden jar, 280 
Light (def.), 167 



350 



INDEX 



Light variation, law of, 174 
Lightning, 284 
Limits of hearing, 138 
Lines of magnetic force, 263 
Liquefaction of gases, 243 
Liquids, 66 

in motion, 90 
Longitudinal and transverse waves, 

132 
Loudness, 151 



Machines, efficiency of, 63 

general law of, 63 

simple, 56 
Magdeburg hemispheres, 114 
Magnetic fields, complex, 267 

effects of currents, 302 

permeability, 268 

storms, 267 
Magnetism, 258 

nature of, 261 
Magneto machine, 316 
Magnets, lifting, 330 
Magnifying glass, 190 

power, 195 
Malleability, 17 
Manometric flames, 149 
Mass, 12 
Matter (def.), 10 

states of, 66 
Measurement, 11 

electric, 334 

of forces, 24 
Mechanical equivalent of heat, 231 
Media for sound, 137 
Megaphone, 141 
Melting point, 233 
Microscope, 194 
Mirage, 186 

Mirror surface (def.), 177 
Molecule, 12 
Moment of a force, 29 

of inertia, 38 
Momentum, 25 
Motion, 19 

first law of, 24 

periodic, 52 

second law of, 27 

simple harmonic, 122 

third law of, 28 



Multiple reflections, 177 
Musical sound (def.), 145 
scales, 161 



Near-sightedness, 193 

Neutral equilibrium, 35 

Newton, 13 

his laws of motion, 24, 27, 28 
his theory of light, 168 

Noise, (def.), 145 



Ohm, 295 
Ohm's law, 298 
Optical density, 184 

instruments, 191 
Organ pipes, 155 
Oscillatory discharge, 282 
Osmosis, 72 



Parallel connection of cells, 297 

forces, 29 
Parallelogram of forces, 26 
Pascal's vases, 76 
Pendulum, 52 
Penumbra, 170 
Periodic motion, 121 
Perpetual motion, 41 
Phase, 125 
Photometry, 174 
Physical state, 11 
Pin-hole image, 172 
Pitch, 145 
Plane mirror, 176 

waves, 171 
Polarization of cell, 287 

of light, 215 
Pole, magnetic, 259 

unit, 261 
Porosity, 15 

Positive and negative in the cir- 
cuit, 288 
Potential, electric, 276 

energy, 37 
Pressure, 72 

effect of, on boiling point, 240 
on freezing point, 234 
on gases, 98 



INDEX 



351 



Pressure transmitted by liquids, 

73 
Prism, 187 
Projectiles, 45 
Projecting lantern, 191 
Proof plane, 279 
Properties of matter, 9 
Pulley, 59 
Pump, air-, 112 

common, 116 

force, 117 

rotary, 117 



Quality of sound, 149 



Radiation, 249 
Radio-activity, 341 
Radium, 344 
Rainbow, 208 
Ram, hydraulic, 94 
Rays of light, 170 
Real image, 180 
Reeds, 157 

Reflecting telescope, 197 
Reflection, law of, 175 

total, 184 
Refraction, 183 

double, 215 
Regelation, 235 
Relay, 329 
Residual charge, 281 
Resistance of the air, 49 

electrical, 294 

internal, 298 

specific, 295 

unit of, 295 
Resolution of forces, 26 

of velocities, 23 
Resonance, 152 
Rigidity, 18 
Ripples, 130 
Rontgen rays, 342 
Rotation, 19 



Scales, thermometer, 221 
Science (def.), 9 
Screw, 61 

Selective absorption, 251 
23 



Self-induction, 315 
Series connection of cells, 297 
Shadows, 196 
Shunt winding, 320 
Simple harmonic motion, 122 
Siphon, 115 
Siren, 146 
Solutions, 236 
Sound (def.), 137 
Sounding bodies, 138 
Spark, electric, 280 
Speaking tubes, 141 
Spectroscope, 203 
Specific gravity of gases, 101 
of liquids and solids, 87 

heat, 229 

inductive capacity, 279 
Spectra, three classes, 206 
Spectrum (def.), 199 

analysis, 205 

invisible, 200 

pure, 202 
Speed (def.), 20 

of light, 172 

of longitudinal waves, 133 

of sound, 139 

of water waves, 129 
Spherical mirrors, 178 
Spirit level, 68 
Stability, 34 
Static electricity, 270 
Stationary waves, 135 
Steam engine, 252 

heating, 249 

turbine, 255 
Stereoscope, 198 
String telephone, 140 
Substance (def.), 10 
Surface tension, 70 
Sympathetic vibrations, 15 



Tables : 

Altitudes by the barometer, 108 
Baume hydrometer scale, 88 
Coefficients of expansion, 227 
Heat conductivity, 248 
Indices of refraction, 187 
Resistivity, electric, 295 
Specific gravity of gases, 101 
Specific heats, 230 



352 



INDEX 



Tables : 

Velocity and space; falling bod- 
ies, 46 
Talking machines, 143 
Telegraph, 327-329 
Telephone, 332 
Telescope, 184 
Temperature, 219 
Tempering, 18 
Tenacity, 17 

Thermo-electric currents, 311 
Thermometers, 220 
Thermometer scales, 221 
Torricelli's experiment, 104 
Toughness, 17 
Train of wheels, 58 
Transformations of energy, 38 
Transformers, 326 
Translation, 19 
Transmitter, carbon, 333 
Turbine water-wheel, 93 

steam, 255 



Unit, current strength, 298 
electric charge, 275 
force, 24 
heat, 229 
illumination, 174 
length, 12 
magnet pole, 261 
mass, 13 
power, 40 
weight, 14 



Unit, work and energy, 36 
Units, electro-magnetic, C. G. S. 
system, 334 

Vacuum bell, 137 

Vaporization, latent heat of, 242 

Vapor pressure, 239 

Variable acceleration, 121 

Vector (def.), 20 

Velocity (def.), 20 

Vibrating strings, laws of, 157 

Virtual image, 180 

Visual angle, 176 

Vocal organs, 159 

Volt, 296 

meter, 308 
Volta's pile, 286 

Water-wheels, 92 
Waves, 127 
Wedge, 61 
Weight, 13 

Wheatstone's bridge, 335 
Wheel and axle, 57 
Wheels, train of, 58 
Windmills, 110 
Wireless telegraphy, 340 
Work, 36 

X-rays, 342 

Zero, absolute, 227 



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